Chapter 18. Semi-Regular Polyhedra

Rovenski Vladimir, Haifa

The way to define an Archimedean solid in Maple Release 5 is to use the command Archimedean(gon,sch,o,r) ; or

PolyhedronName(gon,o,r); from the library geom3d where PolyhedronName is one of

TruncatedTetrahedron, TruncatedOctahedron, TruncatedHexahedron, TruncatedIcosahedron, TruncatedDodecahedron,

SmallRhombicuboctahedron, SmallRhombiicosidodecahedron, GreatRhombicuboctahedron, TruncatedCuboctahedron,

GreatRhombiicosidodecahedron, TruncatedIcosidodecahedron, SnubCube, cuboctahedron, icosidodecahedron .

For example, we define a truncated tetrahedron with center (0,0,0), radius of the circum-sphere 1

> with(geom3d): TruncatedTetrahedron(t,point(o,0,0,0),1):

Warning, existing definition for polar has been overwritten

where gon is the name of the polyhedron to be defined, sch the Schlafli symbol, o the center of the polyhedron.

To access the information relating to an Archimedean solid gon , we use the corresponding function calls.

In Maple Release 5 , one can define the dual of a given polyhedron geom3d[duality](dgon, gon, s) .

For a given regular solid, its dual is also a regular solid. Archimedean solids are also included in this case.

18.2 Programs for Semi-Regular Polyhedra

33334

> restart: c:=1: v:=0.7044022*c: u:=0.4524646*c: # 33334

> a[1]:=[-c+u,c,-c+v]: a[2]:=[-c+v,c,c-u]: a[3]:=[c-u,c,c-v]: a[4]:=[c-v,c,-c+u]: a[5]:=[c,c-u,-c+v]: a[6]:=[c,-c+v,-c+u]: a[7]:=[c,-c+u,c-v]: a[8]:=[c,c-v,c-u]: a[9]:=[c-v,c-u,c]: a[10]:=[c-u,-c+v,c]: a[11]:=[-c+v,-c+u,c]: a[12]:=[-c+u,c-v,c]: a[13]:=[-c+v,c-u,-c]: a[14]:=[-c+u,-c+v,-c]: a[15]:=[c-v,-c+u,-c]: a[16]:=[c-u,c-v,-c]: a[17]:=[-c,c-v,-c+u]: a[18]:=[-c,c-u,c-v]: a[19]:=[-c,-c+v,c-u]: a[20]:=[-c,-c+u,-c+v]: a[21]:=[c-u,-c,-c+v]: a[22]:=[-c+v,-c,-c+u]: a[23]:=[-c+u,-c,c-v]: a[24]:=[c-v,-c,c-u]:

> for i from 1 to 6 do g[i]:=[seq(a[4*(i-1)+j],j=1..4)] od:

> g[7]:=[a[4],a[5],a[3]]: g[8]:=[a[3],a[9],a[2]]: g[9]:=[a[2],a[18],a[1]]: g[10]:=[a[4],a[1],a[13]]: g[11]:=[a[8],a[3],a[5]]: g[12]:=[a[7],a[10],a[8]]: g[13]:=[a[6],a[21],a[7]]: g[14]:=[a[5],a[16],a[6]]: g[15]:=[a[9],a[8],a[10]]: g[16]:=[a[12],a[2],a[9]]: g[17]:=[a[11],a[19],a[12]]: g[18]:=[a[11],a[10],a[24]]: g[19]:=[a[13],a[17],a[14]]: g[20]:=[a[13],a[16],a[4]]: g[21]:=[a[16],a[15],a[6]]: g[22]:=[a[15],a[14],a[22]]: g[23]:=[a[24],a[23],a[11]]: g[24]:=[a[23],a[22],a[20]]: g[25]:=[a[21],a[15],a[22]]: g[26]:=[a[21],a[24],a[7]]: g[27]:=[a[19],a[18],a[12]]: g[28]:=[a[17],a[1],a[18]]: g[29]:=[a[17],a[20],a[14]]: g[30]:=[a[20],a[19],a[23]]: g[31]:=[a[9],a[3],a[8]]: g[32]:=[a[10],a[7],a[24]]: g[33]:=[a[11],a[23],a[19]]: g[34]:=[a[18],a[2],a[12]]: g[35]:=[a[4],a[16],a[5]]: g[36]:=[a[13],a[1],a[17]]: g[37]:=[a[22],a[14],a[20]]: g[38]:=[a[6],a[15],a[21]]:

> P:=j -> plots[polygonplot3d]([seq(g[i], i=1..38)], orientation=[20*j,50], style=PATCH):

> plots[display]([seq(P(j), j=1..18)], insequence=true,scaling=constrained);

> plots[display](plottools[stellate](POLYGONS(seq(g[i],i=1..38))), style=patch, lightmodel=light2);

3434

> restart: c:=1: # 3434

> a[1]:=[c,c,0]: a[2]:=[c,0,-c]: a[3]:=[0,c,-c]: a[4]:=[-c,0,-c]: a[5]:=[-c,c,0]: a[6]:=[-c,0,c]: a[7]:=[-c,-c,0]: a[8]:=[0,c,c]: a[9]:=[0,-c,c]: a[10]:=[c,-c,0]: a[11]:=[c,0,c]: a[12]:=[0,-c,-c]:

> g[1]:=[a[1],a[2],a[3]]: g[2]:=[a[5],a[3],a[4]]: g[3]:=[a[7],a[4],a[12]]: g[4]:=[a[10],a[12],a[2]]: g[5]:=[a[8],a[11],a[1]]: g[6]:=[a[8],a[5],a[6]]: g[7]:=[a[9],a[6],a[7]]: g[8]:=[a[11],a[9],a[10]]: g[9]:=[a[1],a[8],a[5],a[3]]:g[10]:=[a[3],a[4],a[12],a[2]]: g[11]:=[a[12],a[7],a[9],a[10]]: g[12]:=[a[9],a[6],a[8],a[11]]: g[13]:=[a[2],a[10],a[11],a[1]]: g[14]:=[a[5],a[6],a[7],a[4]]:

> P:=j -> plots[polygonplot3d]([seq(g[i], i=1..14)], orientation=[20*j,50], style=PATCH):

> plots[display]([seq(P(j), j=1..18)], insequence=true, scaling=constrained);

> plots[display](plottools[stellate](POLYGONS(seq(g[i],i=1..13))), style=patch, lightmodel=light2, scaling=constrained);

3444-1

> restart: # 3434-1

> c:=1: d:=evalf((c*sqrt(2))/(2+sqrt(2))):

> a[1]:=[d,d,c]: a[2]:=[-d,d,c]: a[3]:=[-d,-d,c]: a[4]:=[d,-d,c]: a[5]:=[c,d,d]: a[6]:=[c,d,-d]: a[7]:=[c,-d,-d]: a[8]:=[c,-d,d]: a[9]:=[-d,c,d]: a[10]:=[-d,c,-d]: a[11]:=[d,c,-d]: a[12]:=[d,c,d]: a[13]:=[d,-c,d]: a[14]:=[d,-c,-d]: a[15]:=[-d,-c,-d]: a[16]:=[-d,-c,d]: a[17]:=[-c,-d,d]: a[18]:=[-c,-d,-d]: a[19]:=[-c,d,-d]: a[20]:=[-c,d,d]: a[21]:=[d,d,-c]: a[22]:=[-d,d,-c]: a[23]:=[-d,-d,-c]: a[24]:=[d,-d,-c]:

> for i from 1 to 6 do g[i]:=[seq(a[4*(i-1)+j],j=1..4)] od:

> g[7]:=[a[1],a[4],a[8],a[5]]: g[8]:=[a[4],a[13],a[16],a[3]]: g[9]:=[a[3],a[17],a[20],a[2]]: g[10]:=[a[2],a[9],a[12],a[1]]: g[11]:=[a[12],a[5],a[6],a[11]]: g[12]:=[a[8],a[13],a[14],a[7]]: g[13]:=[a[16],a[17],a[18],a[15]]: g[14]:=[a[20],a[9],a[10],a[19]]: g[15]:=[a[6],a[7],a[24],a[21]]: g[16]:=[a[14],a[15],a[23],a[24]]: g[17]:=[a[18],a[23],a[22],a[19]]: g[18]:=[a[10],a[11],a[21],a[22]]: g[19]:=[a[1],a[12],a[5]]:g[20]:=[a[4],a[8],a[13]]: g[21]:=[a[3],a[16],a[17]]:g[22]:=[a[2],a[20],a[9]]: g[23]:=[a[6],a[11],a[21]]:g[24]:=[a[7],a[24],a[14]]: g[25]:=[a[15],a[23],a[18]]:g[26]:=[a[19],a[22],a[10]]:

> P:=j -> plots[polygonplot3d]([seq(g[i], i=1..26)], orientation=[20*j,50], style=PATCH):

> plots[display]([seq(P(j), j=1..18)], insequence=true,scaling=constrained);

> plots[display](plottools[stellate](POLYGONS(seq(g[i],i=1..26))), style=patch, lightmodel=light2, scaling=constrained);

3535

> restart: # 3535

> c:=1: p:=evalf(c*((sqrt(5)-1)/2)): v:=p/2:

> a[1]:=[c/2,c+v,c/2+v]: a[2]:=[0,c+p,0]: a[3]:=[c/2,c+v,-c/2-v]: a[4]:=[c+v,c/2+v,-c/2]: a[5]:=[c+v,c/2+v,c/2]: a[6]:=[c/2+v,c/2,c+v]: a[7]:=[c/2+v,-c/2,c+v]: a[8]:=[c+v,-c/2-v,c/2]: a[9]:=[c+p,0,0]: a[10]:=[c/2+v,-c/2,-c-v]: a[11]:=[c/2,-c-v,-c/2-v]: a[12]:=[0,-c-p,0]: a[13]:=[c/2,-c-v,c/2+v]: a[14]:=[-c/2,-c-v,c/2+v]: a[15]:=[-c/2-v,-c/2,c+v]: a[16]:=[0,0,c+p]: a[17]:=[-c/2-v,c/2,c+v]: a[18]:=[-c/2,c+v,c/2+v]: a[19]:=[-c-v,c/2+v,c/2]: a[20]:=[-c-v,c/2+v,-c/2]: a[21]:=[-c/2,c+v,-c/2-v]: a[22]:=[-c/2-v,c/2,-c-v]: a[23]:=[0,0,-c-p]: a[24]:=[c/2+v,c/2,-c-v]: a[25]:=[-c/2-v,-c/2,-c-v]: a[26]:=[-c/2,-c-v,-c/2-v]: a[27]:=[-c-v,-c/2-v,-c/2]: a[28]:=[-c-p,0,0]: a[29]:=[-c-v,-c/2-v,c/2]: a[30]:=[c+v,-c/2-v,-c/2]:

> g[1]:=[a[1],a[2],a[18]]: g[2]:=[a[2],a[3],a[21]]: g[3]:=[a[1],a[6],a[5]]: g[4]:=[a[17],a[18],a[19]]: g[5]:=[a[7],a[6],a[16]]: g[6]:=[a[16],a[17],a[15]]: g[7]:=[a[7],a[13],a[8]]: g[8]:=[a[14],a[15],a[29]]: g[9]:=[a[4],a[24],a[3]]: g[10]:=[a[20],a[21],a[22]]: g[11]:=[a[14],a[12],a[13]]: g[12]:=[a[26],a[11],a[12]]: g[13]:=[a[5],a[9],a[4]]: g[14]:=[a[9],a[8],a[30]]: g[15]:=[a[19],a[20],a[28]]: g[16]:=[a[28],a[27],a[29]]: g[17]:=[a[23],a[24],a[10]]: g[18]:=[a[22],a[23],a[25]]: g[19]:=[a[25],a[26],a[27]]: g[20]:=[a[30],a[11],a[10]]: g[21]:=[a[6],a[1],a[18],a[17],a[16]]: g[22]:=[a[7],a[16],a[15],a[14],a[13]]: g[23]:=[a[3],a[24],a[23],a[22],a[21]]: g[24]:=[a[23],a[10],a[11],a[26],a[25]]: g[25]:=[a[3],a[2],a[1],a[5],a[4]]: g[26]:=[a[2],a[21],a[20],a[19],a[18]]: g[27]:=[a[27],a[26],a[12],a[14],a[29]]: g[28]:=[a[12],a[11],a[30],a[8],a[13]]: g[29]:=[a[8],a[9],a[5],a[6],a[7]]: g[30]:=[a[4],a[9],a[30],a[10],a[24]]: g[31]:=[a[20],a[22],a[25],a[27],a[28]]: g[32]:=[a[19],a[28],a[29],a[15],a[17]]:

> P:=j -> plots[polygonplot3d]([seq(g[i], i=1..32)], orientation=[20*j,50], style=PATCH):

> plots[display]([seq(P(j), j=1..18)], insequence=true, scaling=constrained);

> plots[display](plottools[stellate](POLYGONS(seq(g[i],i=1..32))), style=patch, lightmodel=light2, scaling=constrained);

366

> restart: c:=1: d:=c/3: # 366

> a[1]:=[d,c,-d]: a[2]:=[c,d,-d]: a[3]:=[d,d,-c]: a[4]:=[-d,d,c]: a[5]:=[-d,c,d]: a[6]:=[-c,d,d]: a[7]:=[c,-d,d]: a[8]:=[d,-d,c]: a[9]:=[d,-c,d]: a[10]:=[-d,-d,-c]: a[11]:=[-c,-d,-d]: a[12]:=[-d,-c,-d]:

> g[1]:=[a[1],a[2],a[3]]: g[2]:=[a[4],a[5],a[6]]: g[3]:=[a[7],a[8],a[9]]: g[4]:=[a[10],a[11],a[12]]: g[5]:=[a[2],a[7],a[8],a[4],a[5],a[1]]: g[6]:=[a[2],a[7],a[9],a[12],a[10],a[3]]: g[7]:=[a[8],a[9],a[12],a[11],a[6],a[4]]: g[8]:=[a[10],a[11],a[6],a[5],a[1],a[3]]:

> P:=j -> plots[polygonplot3d]([seq(g[i], i=1..8)], orientation=[20*j,50], style=PATCH):

> plots[display]([seq(P(j), j=1..18)], insequence=true, scaling=constrained);

> plots[display](plottools[stellate](POLYGONS(seq(g[i],i=1..8))), style=patch, lightmodel=light2, scaling=constrained);

388

> restart: c:=1: d:=evalf((2*c)/(2+sqrt(2))): # 388

> a[1]:=[c,c,c-d]: a[2]:=[c,c,d-c]: a[3]:=[-c,c,c-d]: a[4]:=[-c,c,d-c]: a[5]:=[c,-c,c-d]: a[6]:=[c,-c,d-c]: a[7]:=[-c,-c,c-d]: a[8]:=[-c,-c,d-c]: a[9]:=[c,c-d,c]: a[10]:=[c,d-c,c]: a[11]:=[c,c-d,-c]: a[12]:=[c,d-c,-c]: a[13]:=[-c,d-c,-c]: a[14]:=[-c,c-d,-c]: a[15]:=[-c,d-c,c]: a[16]:=[-c,c-d,c]: a[17]:=[c-d,c,-c]: a[18]:=[d-c,c,-c]: a[19]:=[c-d,c,c]: a[20]:=[d-c,c,c]: a[21]:=[c-d,-c,c]: a[22]:=[d-c,-c,c]:a[23]:=[c-d,-c,-c]:a[24]:=[d-c,-c,-c]:

> g[1]:=[a[17],a[2],a[11]]: g[2]:=[a[9],a[19],a[1]]: g[3]:=[a[12],a[23],a[6]]: g[4]:=[a[5],a[10],a[21]]: g[5]:=[a[8],a[13],a[24]]: g[6]:=[a[7],a[22],a[15]]: g[7]:=[a[4],a[14],a[18]]: g[8]:=[a[3],a[20],a[16]]: g[9]:=[a[13],a[8],a[7],a[15],a[16],a[3],a[4],a[14]]: g[10]:=[a[23],a[6],a[5],a[21],a[22],a[7],a[8],a[24]]: g[11]:=[a[12],a[6],a[5],a[10],a[9],a[1],a[2],a[11]]: g[12]:=[a[17],a[2],a[1],a[19],a[20],a[3],a[4],a[18]]: g[13]:=[a[11],a[12],a[23],a[24],a[13],a[14],a[18],a[17]]: g[14]:=[a[10],a[9],a[19],a[20],a[16],a[15],a[22],a[21]]:

> P:=j -> plots[polygonplot3d]([seq(g[i], i=1..14)], orientation=[20*j,50], style=PATCH):

> plots[display]([seq(P(j), j=1..18)], insequence=true, scaling=constrained);

> plots[display](plottools[stellate](POLYGONS(seq(g[i],i=1..14))), style=patch, lightmodel=light2 ,scaling=constrained);

3-10-10

> restart: c:=1: p:=evalf((sqrt(5)-1)*c/2): # 3-10-10

> m:=evalf((c*(sqrt(5)-1))/(2+2*sin(54*Pi/180))): k:=evalf(c*(sqrt(5)-1)-2*m): d:=evalf(p*(c*(sqrt(5)-1)-m)/(c*(sqrt(5)-1))): t:=evalf(m*p/(c*(sqrt(5)-1))): r:=evalf(m*cos(72*Pi/180)):

> x[1]:=c-k/2: y[1]:=c-r: z[1]:=c+t: x[2]:=k/2: y[2]:=p+r: z[2]:=c+d: x[3]:=0: y[3]:=p-m: z[3]:=c+p: x[4]:=0: y[4]:=-p+m: z[4]:=c+p: x[5]:=k/2: y[5]:=-p-r: z[5]:=c+d: x[6]:=c-k/2: y[6]:=r-c: z[6]:=c+t: x[7]:=c+t: y[7]:=-c+k/2: z[7]:=c-r: x[8]:=c+d: y[8]:=-k/2: z[8]:=p+r: x[9]:=c+d: y[9]:=k/2: z[9]:=p+r: x[10]:=c+t: y[10]:=c-k/2: z[10]:=c-r: x[11]:=c-r: y[11]:=c+t: z[11]:=c-k/2: x[12]:=p+r: y[12]:=c+d: z[12]:=k/2: x[13]:=p+r: y[13]:=c+d: z[13]:=-k/2: x[14]:=c-r: y[14]:=c+t: z[14]:=-c+k/2: x[15]:=c+t: y[15]:=c-k/2: z[15]:=r-c: x[16]:=c+d: y[16]:=k/2: z[16]:=-p-r: x[17]:=c+p: y[17]:=0: z[17]:=-p+m: x[18]:=c+p: y[18]:=0: z[18]:=p-m: x[19]:=c+d: y[19]:=-k/2: z[19]:=-p-r: x[20]:=c+t: y[20]:=-c+k/2: z[20]:=r-c: x[21]:=x[14]: y[21]:=-y[14]: z[21]:=z[14]: x[22]:=x[13]: y[22]:=-y[13]: z[22]:=z[13]: x[23]:=x[22]: y[23]:=y[22]: z[23]:=-z[22]: x[24]:=x[21]: y[24]:=y[21]: z[24]:=-z[21]: x[25]:=p-m: y[25]:=-c-p: z[25]:=0: x[26]:=-p+m: y[26]:=-c-p: z[26]:=0: x[27]:=-x[22]: y[27]:=y[22]: z[27]:=z[22]: x[28]:=-x[21]: y[28]:=y[21]: z[28]:=z[21]: x[29]:=-x[32]: y[29]:=y[32]: z[29]:=z[32]: x[30]:=-x[31]: y[30]:=y[31]: z[30]:=z[31]: x[31]:=x[5]: y[31]:=y[5]: z[31]:=-z[5]: x[32]:=x[6]: y[32]:=y[6]: z[32]:=-z[6]: x[33]:=x[1]: y[33]:=y[1]: z[33]:=-z[1]: x[34]:=x[2]: y[34]:=y[2]: z[34]:=-z[2]: x[35]:=-x[34]: y[35]:=y[34]: z[35]:=z[34]: x[36]:=-x[33]: y[36]:=y[33]: z[36]:=z[33]: x[37]:=-x[14]: y[37]:=y[14]: z[37]:=z[14]: x[38]:=-x[13]: y[38]:=y[13]: z[38]:=z[13]: x[39]:=x[26]: y[39]:=c+p: z[39]:=0: x[40]:=x[25]: y[40]:=c+p: z[40]:=0: x[41]:=x[3]: y[41]:=y[3]: z[41]:=-z[3]: x[42]:=x[4]: y[42]:=y[4]: z[42]:=-z[4]: x[43]:=-x[12]: y[43]:=y[12]: z[43]:=z[12]: x[44]:=-x[11]: y[44]:=y[11]: z[44]:=z[11]: x[45]:=-x[10]: y[45]:=y[10]: z[45]:=z[10]: x[46]:=-x[9]: y[46]:=y[9]: z[46]:=z[9]: x[47]:=-x[8]: y[47]:=y[8]: z[47]:=z[8]: x[48]:=-x[7]: y[48]:=y[7]: z[48]:=z[7]: x[49]:=-x[6]: y[49]:=y[6]: z[49]:=z[6]: x[50]:=-x[5]: y[50]:=y[5]: z[50]:=z[5]: x[51]:=-x[2]: y[51]:=y[2]: z[51]:=z[2]: x[52]:=-x[18]: y[52]:=0: z[52]:=z[18]: x[53]:=-x[17]: y[53]:=0: z[53]:=z[17]: x[54]:=-x[19]: y[54]:=y[19]: z[54]:=z[19]: x[55]:=-x[20]: y[55]:=y[20]: z[55]:=z[20]: x[56]:=x[27]: y[56]:=y[27]: z[56]:=-z[27]: x[57]:=x[28]: y[57]:=y[28]: z[57]:=-z[28]: x[58]:=-x[1]: y[58]:=y[1]: z[58]:=z[1]: x[59]:=-x[15]: y[59]:=y[15]: z[59]:=z[15]: x[60]:=-x[16]: y[60]:=y[16]: z[60]:=z[16]:

> for i from 1 to 60 do a[i]:=[x[i],y[i],z[i]] od:

> g[1]:=[a[1],a[2],a[3],a[4],a[5],a[6],a[7],a[8],a[9],a[10]]: g[2]:=[a[3],a[4],a[50],a[49],a[48],a[47],a[46],a[45],a[58],a[51]]: g[3]:=[a[15],a[16],a[19],a[20],a[32],a[31],a[42],a[41],a[34],a[33]]: g[4]:=[a[41],a[42],a[30],a[29],a[55],a[54],a[60],a[59],a[36],a[35]]: g[5]:=[a[7],a[8],a[18],a[17],a[19],a[20],a[21],a[22],a[23],a[24]]: g[6]:=[a[9],a[18],a[17],a[16],a[15],a[14],a[13],a[12],a[11],a[10]]: g[7]:=[a[59],a[60],a[53],a[52],a[46],a[45],a[44],a[43],a[38],a[37]]: g[8]:=[a[53],a[54],a[55],a[28],a[27],a[56],a[57],a[48],a[47],a[52]]: g[9]:=[a[14],a[33],a[34],a[35],a[36],a[37],a[38],a[39],a[40],a[13]]: g[10]:=[a[11],a[12],a[40],a[39],a[43],a[44],a[58],a[51],a[2],a[1]]: g[11]:=[a[29],a[30],a[31],a[32],a[21],a[22],a[25],a[26],a[27],a[28]]: g[12]:=[a[25],a[23],a[24],a[6],a[5],a[50],a[49],a[57],a[56],a[26]]: g[13]:=[a[1],a[10],a[11]]: g[14]:=[a[2],a[51],a[3]]: g[15]:=[a[58],a[44],a[45]]: g[16]:=[a[46],a[52],a[47]]: g[17]:=[a[48],a[57],a[49]]: g[18]:=[a[4],a[50],a[5]]: g[19]:=[a[6],a[24],a[7]]: g[20]:=[a[8],a[18],a[9]]: g[21]:=[a[12],a[13],a[40]]: g[22]:=[a[43],a[39],a[38]]: g[23]:=[a[27],a[26],a[56]]: g[24]:=[a[22],a[23],a[25]]: g[25]:=[a[19],a[16],a[17]]: g[26]:=[a[15],a[33],a[14]]: g[27]:=[a[34],a[41],a[35]]: g[28]:=[a[36],a[59],a[37]]: g[29]:=[a[60],a[54],a[53]]: g[30]:=[a[55],a[29],a[28]]: g[31]:=[a[31],a[30],a[42]]: g[32]:=[a[21],a[32],a[20]]:

> P:=j -> plots[polygonplot3d]([seq(g[i], i=1..32)], orientation=[20*j,50], style=PATCH):

> plots[display]([seq(P(j), j=1..18)], insequence=true, scaling=constrained);

> plots[display](plottools[stellate](POLYGONS(seq(g[i],i=1..32))), style=patch, lightmodel=light2, scaling=constrained);

466

> restart: c:=1: t:=evalf(c/3): u:=evalf(c-t): # 466

> a[1]:=[0,u,t]: a[2]:=[-t,u,0]: a[3]:=[0,u,-t]: a[4]:=[t,u,0]: a[5]:=[u,0,t]: a[6]:=[u,t,0]: a[7]:=[u,0,-t]: a[8]:=[u,-t,0]: a[9]:=[0,-u,t]: a[10]:=[t,-u,0]: a[11]:=[0,-u,-t]: a[12]:=[-t,-u,0]: a[13]:=[-u,0,t]: a[14]:=[-u,-t,0]: a[15]:=[-u,0,-t]: a[16]:=[-u,t,0]: a[17]:=[t,0,u]: a[18]:=[0,t,u]: a[19]:=[-t,0,u]: a[20]:=[0,-t,u]: a[21]:=[t,0,-u]: a[22]:=[0,t,-u]: a[23]:=[-t,0,-u]: a[24]:=[0,-t,-u]:

> for i from 1 to 6 do g[i]:=[seq(a[4*(i-1)+j],j=1..4)] od:

> g[7]:=([a[5],a[17],a[18],a[1],a[4],a[6]]): g[8]:=([a[10],a[9],a[20],a[17],a[5],a[8]]): g[9]:=([a[11],a[24],a[23],a[15],a[14],a[12]]): g[10]:=([a[23],a[15],a[16],a[2],a[3],a[22]]): g[11]:=([a[1],a[2],a[16],a[13],a[19],a[18]]): g[12]:=([a[9],a[20],a[19],a[13],a[14],a[12]]): g[13]:=([a[7],a[21],a[24],a[11],a[10],a[8]]): g[14]:=([a[6],a[7],a[21],a[22],a[3],a[4]]):

> P:=j -> plots[polygonplot3d]([seq(g[i], i=1..14)], orientation=[20*j,50], style=PATCH):

> plots[display]([seq(P(j), j=1..18)], insequence=true, scaling=constrained);

> plots[display](plottools[stellate](POLYGONS(seq(g[i],i=1..13))), style=patch, lightmodel=light2, scaling=constrained);

566

> restart: # 566

> c:=1: t:=evalf(c/3): p:=evalf(c*(sqrt(5)-1)/2): d:=evalf(p/3): v:=evalf((c+2*p)/3): m:=evalf((2*c+p)/3):

> a[1]:=[d,0,c]: a[2]:=[2*d,t,m]: a[3]:=[v,d, c-t]: a[4]:=[v,-d,c-t]: a[5]:=[2*d,-t, m]: a[6]:=[d,0,-c]: a[7]:=[2*d,t,-m]: a[8]:=[v,d,t-c]: a[9]:=[v,-d,t-c]: a[10]:=[2*d,-t,-m]: a[11]:=[-d,0,c]: a[12]:=[-2*d,t,m]: a[13]:=[-v,d,c-t]: a[14]:=[-v,-d,c-t]: a[15]:=[-2*d,-t,m]: a[16]:=[-d,0,-c]: a[17]:=[-2*d,t,-m]: a[18]:=[-v,d,t-c]: a[19]:=[-v,-d,t-c]: a[20]:=[-2*d,-t,-m]: a[21]:=[-t,m,2*d]: a[22]:=[-d,c-t,v]: a[23]:=[d,c-t,v]: a[24]:=[t,m,2*d]: a[25]:=[0,c,d]: a[26]:=[-t,m,-2*d]: a[27]:=[-d,c-t,-v]: a[28]:=[d,c-t,-v]: a[29]:=[t,m,-2*d]: a[30]:=[0,c,-d]: a[31]:=[-t,-m,2*d]: a[32]:=[-d,t-c,v]: a[33]:=[d,t-c,v]: a[34]:=[t,-m,2*d]: a[35]:=[0,-c,d]: a[36]:=[-t,-m,-2*d]: a[37]:=[-d,t-c,-v]: a[38]:=[d,t-c,-v]: a[39]:=[t,-m,-2*d]: a[40]:=[0,-c,-d]: a[41]:=[c-t,v,d]: a[42]:=[m,2*d,t]: a[43]:=[c,d,0]: a[44]:=[m,2*d,-t]: a[45]:=[c-t,v,-d]: a[46]:=[t-c,v,d]: a[47]:=[-m,2*d,t]: a[48]:=[-c,d,0]: a[49]:=[-m,2*d,-t]: a[50]:=[t-c,v,-d]: a[51]:=[c-t,-v,d]: a[52]:=[m,-2*d,t]: a[53]:=[c,-d,0]: a[54]:=[m,-2*d,-t]: a[55]:=[c-t,-v,-d]: a[56]:=[t-c,-v,d]: a[57]:=[-m,-2*d,t]: a[58]:=[-c,-d,0]: a[59]:=[-m,-2*d,-t]: a[60]:=[t-c,-v,-d]:

> for i from 1 to 12 do g[i]:=[seq(a[5*(i-1)+j],j=1..5)] od:

> g[13]:=[a[11],a[12],a[22],a[23],a[2],a[1]]: g[14]:=[a[5],a[33],a[32],a[15],a[11],a[1]]: g[15]:=[a[23],a[24],a[41],a[42],a[3],a[2]]: g[16]:=[a[42],a[43],a[53],a[52],a[4],a[3]]: g[17]:=[a[52],a[51],a[34],a[33],a[5],a[4]]: g[18]:=[a[51],a[55],a[39],a[40],a[35],a[34]]: g[19]:=[a[60],a[56],a[31],a[35],a[40],a[36]]: g[20]:=[a[56],a[57],a[14],a[15],a[32],a[31]]: g[21]:=[a[14],a[57],a[58],a[48],a[47],a[13]]: g[22]:=[a[12],a[13],a[47],a[46],a[21],a[22]]: g[23]:=[a[21],a[46],a[50],a[26],a[30],a[25]]: g[24]:=[a[24],a[25],a[30],a[29],a[45],a[41]]: g[25]:=[a[28],a[7],a[8],a[44],a[45],a[29]]: g[26]:=[a[44],a[8],a[9],a[54],a[53],a[43]]: g[27]:=[a[9],a[10],a[38],a[39],a[55],a[54]]: g[28]:=[a[10],a[6],a[16],a[20],a[37],a[38]]: g[29]:=[a[36],a[37],a[20],a[19],a[59],a[60]]: g[30]:=[a[58],a[59],a[19],a[18],a[49],a[48]]: g[31]:=[a[50],a[49],a[18],a[17],a[27],a[26]]: g[32]:=[a[28],a[27],a[17],a[16],a[6],a[7]]:

> P:=j -> plots[polygonplot3d]([seq(g[i], i=1..32)], orientation=[20*j,50], style=PATCH):

> plots[display]([seq(P(j), j=1..18)], insequence=true, scaling=constrained);

> plots[display](plottools[stellate](POLYGONS(seq(g[i],i=1..32))), style=patch, lightmodel=light2, scaling=constrained);

3454

> restart: c:=1: p:=evalf(c*((sqrt(5)-1)/2)): # 3454

> a[1]:=[c/3,c/3,c+2*p/3]: a[2]:=[(p+c)/3,(2*c+p)/3,2*(c+p)/3]: a[3]:=[0,c+p/3,(2*c+p)/3]: a[4]:=[-(p+c)/3,(c*2+p)/3,(2*p+2*c)/3]: a[5]:=[-c/3,c/3,c+2*p/3]: a[6]:=[-(2*c+p)/3,0,c+p/3]: a[7]:=[-(2*c+2*p)/3,(p+c)/3,(2*c+p)/3]: a[8]:=[-c-2*p/3,c/3,c/3]: a[9]:=[-c-2*p/3,-c/3,c/3]: a[10]:=[-(2*c+2*p)/3,-(c+p)/3,(2*c+p)/3]: a[11]:=[-(2*c+p)/3,(2*c+2*p)/3,(c+p)/3]: a[12]:=[-c/3,c+2*p/3,c/3]: a[13]:=[-c/3,c+2*p/3,-c/3]: a[14]:=[-(2*c+p)/3,(2*c+2*p)/3,-(c+p)/3]: a[15]:=[-c-p/3,(2*c+p)/3,0]: a[17]:=[c+p/3,(2*c+p)/3,0]: a[16]:=[(2*c+p)/3,(2*c+2*p)/3,(c+p)/3]: a[18]:=[(2*c+p)/3,(2*c+2*p)/3,-(c+p)/3]: a[19]:=[c/3,c+2*p/3,-c/3]: a[20]:=[c/3,c+2*p/3,c/3]: a[21]:=[-(c+p)/3,(2*c+p)/3,-(2*c+2*p)/3]: a[22]:=[0,c+p/3,-(2*c+p)/3]: a[23]:=[(c+p)/3,(2*c+p)/3,-(2*c+2*p)/3]: a[24]:=[c/3,c/3,-c-2*p/3]: a[25]:=[-c/3,c/3,-c-2*p/3]: a[26]:=[-(2*c+p)/3,0,-c-p/3]: a[27]:=[-(2*c+2*p)/3,-(c+p)/3,-(2*c+p)/3]: a[28]:=[-c-2*p/3,-c/3,-c/3]: a[29]:=[-c-2*p/3,c/3,-c/3]: a[30]:=[-(2*c+2*p)/3,(c+p)/3,-(2*c+p)/3]: a[31]:=[-c/3,-c/3,c+2*p/3]: a[33]:=[0,-c-p/3,(2*c+p)/3]: a[32]:=[-(c+p)/3,-(2*c+p)/3,(2*c+2*p)/3]: a[34]:=[(c+p)/3,-(2*c+p)/3,(2*c+2*p)/3]: a[35]:=[c/3,-c/3,c+2*p/3]: a[36]:=[(2*c+p)/3,0,c+p/3]: a[37]:=[(2*c+2*p)/3,-(c+p)/3,(2*c+p)/3]: a[38]:=[c+2*p/3,-c/3,c/3]: a[39]:=[c+2*p/3,c/3,c/3]: a[40]:=[(2*c+2*p)/3,(c+p)/3,(2*c+p)/3]: a[41]:=[(2*c+p)/3,-(2*c+2*p)/3,(c+p)/3]: a[42]:=[c/3,-c-2*p/3,c/3]: a[43]:=[c/3,-c-2*p/3,-c/3]: a[44]:=[(2*c+p)/3,-(2*c+2*p)/3,-(c+p)/3]: a[45]:=[c+p/3,-(2*c+p)/3,0]: a[46]:=[c+2*p/3,-c/3,-c/3]: a[47]:=[(2*c+2*p)/3,-(c+p)/3,-(2*c+p)/3]: a[48]:=[(2*c+p)/3,0,-c-p/3]: a[50]:=[c+2*p/3,c/3,-c/3]: a[49]:=[(2*c+2*p)/3,(c+p)/3,-(2*c+p)/3]: a[51]:=[-(c+p)/3,-(2*c+p)/3,-(2*c+2*p)/3]: a[52]:=[-c/3,-c/3,-c-2*p/3]: a[53]:=[c/3,-c/3,-c-2*p/3]: a[54]:=[(c+p)/3,-(2*c+p)/3,-(2*c+2*p)/3]: a[55]:=[0,-c-p/3,-(2*c+p)/3]: a[56]:=[-c/3,-c-2*p/3,-c/3]: a[58]:=[-(2*c+p)/3,-(2*c+2*p)/3,(c+p)/3]: a[59]:=[-c-p/3,-(2*c+p)/3,0]:a[57]:=[-c/3,-c-2*p/3,c/3]: a[60]:=[-(2*c+p)/3,-(2*c+2*p)/3,-(p+c)/3]:

> g[1]:=[a[4],a[11],a[7]]: g[2]:=[a[3],a[20],a[12]]: g[3]:=[a[19],a[22],a[13]]: g[4]:=[a[14],a[21],a[30]]: g[5]:=[a[8],a[15],a[29]]: g[6]:=[a[34],a[41],a[37]]: g[7]:=[a[33],a[57],a[42]]: g[8]:=[a[38],a[45],a[46]]: g[9]:=[a[44],a[54],a[47]]: g[10]:=[a[43],a[56],a[55]]: g[11]:=[a[1],a[35],a[36]]: g[12]:=[a[16],a[2],a[40]]: g[13]:=[a[50],a[17],a[39]]: g[14]:=[a[49],a[23],a[18]]: g[15]:=[a[24],a[48],a[53]]: g[16]:=[a[52],a[26],a[25]]: g[17]:=[a[51],a[60],a[27]]: g[18]:=[a[59],a[9],a[28]]: g[19]:=[a[31],a[5],a[6]]: g[20]:=[a[58],a[32],a[10]]: g[21]:=[a[30],a[11],a[10]]: g[22]:=[a[1],a[2],a[3],a[4],a[5]]: g[23]:=[a[6],a[7],a[8],a[9],a[10]]: g[24]:=[a[11],a[12],a[13],a[14],a[15]]: g[25]:=[a[16],a[17],a[18],a[19],a[20]]: g[26]:=[a[21],a[22],a[23],a[24],a[25]]: g[27]:=[a[26],a[27],a[28],a[29],a[30]]: g[28]:=[a[31],a[32],a[33],a[34],a[35]]: g[29]:=[a[36],a[37],a[38],a[39],a[40]]: g[30]:=[a[41],a[42],a[43],a[44],a[45]]: g[31]:=[a[46],a[47],a[48],a[49],a[50]]: g[32]:=[a[51],a[52],a[53],a[54],a[55]]: g[33]:=[a[56],a[57],a[58],a[59],a[60]]: g[34]:=[a[2],a[16],a[20],a[3]]: g[35]:=[a[3],a[12],a[11],a[4]]: g[36]:=[a[4],a[7],a[6],a[5]]: g[37]:=[a[7],a[11],a[15],a[8]]: g[38]:=[a[15],a[14],a[30],a[29]]: g[39]:=[a[14],a[13],a[22],a[21]]: g[40]:=[a[13],a[12],a[20],a[19]]: g[41]:=[a[19],a[18],a[23],a[22]]: g[42]:=[a[21],a[25],a[26],a[30]]: g[43]:=[a[29],a[28],a[9],a[8]]: g[44]:=[a[35],a[34],a[37],a[36]]: g[45]:=[a[34],a[33],a[42],a[41]]: g[46]:=[a[33],a[32],a[58],a[57]]: g[47]:=[a[57],a[56],a[43],a[42]]: g[48]:=[a[43],a[55],a[54],a[44]]: g[49]:=[a[44],a[47],a[46],a[45]]: g[50]:=[a[45],a[38],a[37],a[41]]: g[51]:=[a[38],a[46],a[50],a[39]]: g[52]:=[a[47],a[54],a[53],a[48]]: g[53]:=[a[55],a[56],a[60],a[51]]: g[54]:=[a[1],a[36],a[40],a[2]]: g[55]:=[a[16],a[40],a[39],a[17]]: g[56]:=[a[17],a[50],a[49],a[18]]: g[57]:=[a[23],a[49],a[48],a[24]]: g[58]:=[a[24],a[53],a[52],a[25]]: g[59]:=[a[26],a[52],a[51],a[27]]: g[60]:=[a[27],a[60],a[59],a[28]]: g[61]:=[a[9],a[59],a[58],a[10]]: g[62]:=[a[10],a[32],a[31],a[6]]: g[63]:=[a[5],a[31],a[35],a[1]]:

> P:=j -> plots[polygonplot3d]([seq(g[i], i=1..63)], orientation=[20*j,50], style=PATCH):

> plots[display]([seq(P(j), j=1..18)], insequence=true, scaling=constrained);

> plots[display](plottools[stellate](POLYGONS(seq(g[i],i=1..63))), style=patch, lightmodel=light2, scaling=constrained);

468

> restart: c:=1: d:=evalf(2*c*(3*sqrt(2)+2)/7): # 468

> m:=evalf(d*(3*sqrt(2)-4)/4):l:=evalf(m+d*(2-sqrt(2))/4): t:=evalf(d*(2-sqrt(2))/4):

> a[1]:=[c-l,-t,c]: a[2]:=[t,-c+l,c]: a[3]:=[-t,-c+l,c]: a[4]:=[-c+l,-t,c]: a[5]:=[-c+l,t,c]: a[6]:=[-t,c-l,c]: a[7]:=[t,c-l,c]: a[8]:=[c-l,t,c]: a[9]:=[c,t,c-l]: a[10]:=[c,-t,c-l]: a[11]:=[c,-c+l,t]: a[12]:=[c,-c+l,-t]: a[13]:=[c,-t,-c+l]: a[14]:=[c,t,-c+l]: a[15]:=[c,c-l,-t]: a[16]:=[c,c-l,t]: a[17]:=[c-l,c,t]: a[18]:=[c-l,c,-t]: a[19]:=[t,c,-c+l]: a[20]:=[-t,c,-c+l]: a[21]:=[-t,c-l,-c]: a[22]:=[t,c-l,-c]: a[23]:=[c-l,t,-c]: a[24]:=[-c+l,t,-c]: a[25]:=[-c+l,c,-t]:a[26]:=[-c,c-l,-t]:a[27]:=[-c,t,-c+l]: a[28]:=[-c,-t,-c+l]:a[29]:=[-c+l,-t,-c]:a[30]:=[-t,c,c-l]: a[31]:=[t,c,c-l]: a[32]:=[-c+l,c,t]: a[33]:=[-c,c-l,t]: a[34]:=[-c,t,c-l]: a[35]:=[-c,-t,c-l]: a[36]:=[-c,-c+l,t]: a[37]:=[-c+l,-c,t]: a[38]:=[-c+l,-c,-t]: a[39]:=[-c,-c+l,-t]: a[40]:=[-t,-c,-c+l]: a[41]:=[-t,-c+l,-c]:a[42]:=[t,-c+l,-c]: a[43]:=[t,-c,-c+l]:a[44]:=[c-l,-c,-t]:a[45]:=[c-l,-t,-c]: a[46]:=[t,-c,c-l]: a[47]:=[-t,-c,c-l]: a[48]:=[c-l,-c,t]:

> g[1]:=([a[1],a[2],a[3],a[4],a[5],a[6],a[7],a[8]]): g[2]:=([a[17],a[18],a[19],a[20],a[25],a[32],a[30],a[31]]): g[3]:=([a[22],a[23],a[45],a[42],a[41],a[29],a[24],a[21]]): g[4]:=([a[37],a[38],a[40],a[43],a[44],a[48],a[46],a[47]]): g[5]:=([a[9],a[10],a[11],a[12],a[13],a[14],a[15],a[16]]): g[6]:=([a[26],a[27],a[28],a[39],a[36],a[35],a[34],a[33]]): g[7]:=([a[5],a[6],a[30],a[32],a[33],a[34]]): g[8]:=([a[3],a[4],a[35],a[36],a[37],a[47]]): g[9]:=([a[1],a[2],a[46],a[48],a[11],a[10]]): g[10]:=([a[7],a[8],a[9],a[16],a[17],a[31]]): g[11]:=([a[20],a[25],a[26],a[27],a[24],a[21]]): g[12]:=([a[28],a[39],a[38],a[40],a[41],a[29]]): g[13]:=([a[14],a[23],a[22],a[19],a[18],a[15]]): g[14]:=([a[12],a[13],a[45],a[42],a[43],a[44]]): g[15]:=([a[6],a[7],a[31],a[30]]): g[16]:=([a[1],a[10],a[9],a[8]]): g[17]:=([a[2],a[3],a[47],a[46]]): g[18]:=([a[4],a[5],a[34],a[35]]): g[19]:=([a[32],a[25],a[26],a[33]]): g[20]:=([a[36],a[37],a[38],a[39]]): g[21]:=([a[11],a[12],a[44],a[48]]): g[22]:=([a[15],a[16],a[17],a[18]]): g[23]:=([a[19],a[20],a[21],a[22]]): g[24]:=([a[27],a[24],a[29],a[28]]): g[25]:=([a[40],a[41],a[42],a[43]]): g[26]:=([a[13],a[14],a[23],a[45]]):

> P:=j -> plots[polygonplot3d]([seq(g[i], i=1..26)], orientation=[20*j,50], style=PATCH):

> plots[display]([seq(P(j), j=1..18)], insequence=true, scaling=constrained);

> plots[display](plottools[stellate](POLYGONS(seq(g[i],i=1..26))), style=patch, lightmodel=light2, scaling=constrained);

4610

> restart: # 4610

> c:=1: p:=evalf((sqrt(5)-1)*c/2): co:=evalf(cos(32)): m:=evalf((c*(sqrt(5)-1))/(2+2*sin(54*Pi/180))): k:=evalf(c*(sqrt(5)-1)-2*m): d:=evalf((2*p-m)/2): t:=m/2: r:=evalf(m*cos(72*Pi/180)): tau:=evalf((sqrt(5)-1)/2):
l:=evalf((tau/(sqrt(3+tau)*(1+tau)+2*tau))):

> x[1]:=c-k/2: y[1]:=c-r+2*l*(r-c): z[1]:=c+t: x[2]:=k/2+l*(c+t-k/2): y[2]:=p+r+l*(k/2-c-p-r): z[2]:=c+d-l*(r+d): x[3]:=l*(c+d): y[3]:=p-m+l*(m-p-k/2): z[3]:=c+p+l*(r-c): x[4]:=x[3]: y[4]:=-y[3]: z[4]:=z[3]: x[5]:=x[2]: y[5]:=-y[2]: z[5]:=z[2]: x[6]:=x[1]: y[6]:=-y[1]: z[6]:=z[1]: x[7]:=c+t+l*(k/2-c-t): y[7]:=k/2-c+l*(p+r-k/2+c): z[7]:=c-r+l*(d+r): x[8]:=c+d-l*(c+d): y[8]:=-k/2+l*(p-m+k/2): z[8]:=p+r+l*(c-r): x[9]:=x[8]: y[9]:=-y[8]: z[9]:=z[8]: x[10]:=x[7]: y[10]:=-y[7]: z[10]:=z[7]: x[11]:=z[7]: y[11]:=x[7]: z[11]:=-y[7]: x[12]:=z[1]: y[12]:=x[1]: z[12]:=y[1]: x[13]:=z[2]: y[13]:=x[2]: z[13]:=y[2]: x[14]:=z[3]: y[14]:=x[3]: z[14]:=y[3]: x[15]:=x[14]: y[15]:=y[14]: z[15]:=-z[14]: x[16]:=x[13]: y[16]:=y[13]: z[16]:=-z[13]: x[17]:=x[12]: y[17]:=y[12]: z[17]:=-z[12]: x[18]:=x[11]: y[18]:=y[11]: z[18]:=-z[11]: x[19]:=z[8]: y[19]:=x[8]: z[19]:=y[8]: x[20]:=x[19]: y[20]:=y[19]: z[20]:=-y[8]: x[21]:=y[2]: y[21]:=z[2]: z[21]:=x[2]: x[22]:=y[3]: y[22]:=z[3]: z[22]:=x[3]: x[23]:=-y[3]: y[23]:=z[3]: z[23]:=x[3]: x[24]:=-y[2]: y[24]:=z[2]: z[24]:=x[2]: x[25]:=-y[1]: y[25]:=z[1]: z[25]:=x[1]: x[26]:=y[7]: y[26]:=z[7]: z[26]:=x[7]: x[27]:=y[8]: y[27]:=z[8]: z[27]:=x[8]: x[28]:=-y[8]: y[28]:=z[8]: z[28]:=x[8]: x[29]:=-y[7]: y[29]:=z[7]: z[29]:=x[7]: x[30]:=y[1]: y[30]:=z[1]: z[30]:=x[1]: x[31]:=y[8]: y[31]:=z[8]: z[31]:=-x[8]: x[32]:=y[7]: y[32]:=z[7]: z[32]:=-x[7]: x[33]:=-y[1]: y[33]:=z[1]: z[33]:=-x[1]: x[34]:=-y[2]: y[34]:=z[2]: z[34]:=-x[2]: x[35]:=-y[3]: y[35]:=z[3]: z[35]:=-x[3]: x[36]:=y[3]: y[36]:=z[3]: z[36]:=-x[3]: x[37]:=-x[34]: y[37]:=y[34]: z[37]:=z[34]: x[38]:=-x[33]: y[38]:=y[33]: z[38]:=z[33]: x[39]:=-y[7]: y[39]:=y[32]: z[39]:=z[32]: x[40]:=-y[8]: y[40]:=y[31]: z[40]:=z[31]: x[41]:=x[3]: y[41]:=y[3]: z[41]:=-z[3]: x[42]:=x[2]: y[42]:=y[2]: z[42]:=-z[2]: x[43]:=x[1]: y[43]:=y[1]: z[43]:=-z[1]: x[44]:=x[7]: y[44]:=-y[7]: z[44]:=-z[7]: x[45]:=x[8]: y[45]:=-y[8]: z[45]:=-z[8]: x[46]:=x[8]: y[46]:=y[8]: z[46]:=-z[8]: x[47]:=x[7]: y[47]:=y[7]: z[47]:=-z[7]: x[48]:=x[1]: y[48]:=-y[1]: z[48]:=-z[1]: x[49]:=x[2]: y[49]:=-y[2]: z[49]:=-z[2]: x[50]:=x[3]: y[50]:=-y[3]: z[50]:=-z[3]: x[51]:=x[11]: y[51]:=-y[11]: z[51]:=-z[11]: x[52]:=x[12]: y[52]:=-y[12]: z[52]:=-z[12]: x[53]:=x[13]: y[53]:=-y[13]: z[53]:=-z[13]: x[54]:=x[14]: y[54]:=-y[14]: z[54]:=-z[14]: x[55]:=x[14]: y[55]:=-y[14]: z[55]:=z[14]: x[56]:=x[13]: y[56]:=-y[13]: z[56]:=z[13]: x[57]:=x[12]: y[57]:=-y[12]: z[57]:=z[12]: x[58]:=x[11]: y[58]:=-y[11]: z[58]:=z[11]: x[59]:=x[19]: y[59]:=-y[19]: z[59]:=z[20]: x[60]:=x[19]: y[60]:=-y[19]: z[60]:=z[19]: x[61]:=x[23]: y[61]:=-y[22]: z[61]:=-z[22]: x[62]:=x[24]: y[62]:=-y[21]: z[62]:=-z[21]: x[63]:=-y[1]: y[63]:=-z[1]: z[63]:=-x[1]: x[64]:=y[7]: y[64]:=-z[7]: z[64]:=-x[7]: x[65]:=y[8]: y[65]:=-y[27]: z[65]:=-z[27]: x[66]:=x[28]: y[66]:=-y[28]: z[66]:=-z[28]: x[67]:=-x[26]: y[67]:=-y[26]: z[67]:=-z[26]: x[68]:=-x[25]: y[68]:=-y[25]: z[68]:=-z[25]: x[69]:=x[21]: y[69]:=-y[21]: z[69]:=-z[21]: x[70]:=y[3]: y[70]:=-z[3]: z[70]:=-x[3]: x[71]:=y[3]: y[71]:=-y[22]: z[71]:=z[22]: x[72]:=x[21]: y[72]:=-y[21]: z[72]:=z[21]: x[73]:=-x[25]: y[73]:=-y[25]: z[73]:=z[25]: x[74]:=-x[26]: y[74]:=-y[26]: z[74]:=z[26]: x[75]:=x[28]: y[75]:=-y[28]: z[75]:=z[28]: x[76]:=y[8]: y[76]:=-y[27]: z[76]:=z[27]: x[77]:=x[26]: y[77]:=-y[26]: z[77]:=z[26]: x[78]:=x[25]: y[78]:=-y[25]: z[78]:=z[25]: x[79]:=x[24]: y[79]:=-y[24]: z[79]:=z[24]: x[80]:=x[23]: y[80]:=-y[23]: z[80]:=z[23]: x[81]:=-z[7]: y[81]:=-x[7]: z[81]:=y[7]: x[82]:=-z[8]: y[82]:=-x[8]: z[82]:=y[8]: x[83]:=-z[8]: y[83]:=-x[8]: z[83]:=-y[8]: x[84]:=-z[7]: y[84]:=-x[7]: z[84]:=-y[7]: x[85]:=-z[1]: y[85]:=-x[1]: z[85]:=y[1]: x[86]:=-z[2]: y[86]:=-x[2]: z[86]:=y[2]: x[87]:=-z[3]: y[87]:=-x[3]: z[87]:=-y[4]: x[88]:=-z[3]: y[88]:=-x[3]: z[88]:=-y[3]: x[89]:=-z[2]: y[89]:=-x[2]: z[89]:=-y[2]: x[90]:=-z[1]: y[90]:=-x[1]: z[90]:=-y[1]: x[91]:=-x[7]: y[91]:=y[7]: z[91]:=-z[7]: x[92]:=-x[8]: y[92]:=y[8]: z[92]:=-z[8]: x[93]:=-x[8]: y[93]:=-y[8]: z[93]:=-z[8]: x[94]:=-x[7]: y[94]:=-y[7]: z[94]:=-z[7]: x[95]:=-x[1]: y[95]:=y[1]: z[95]:=-z[1]: x[96]:=-x[2]: y[96]:=y[2]: z[96]:=-z[2]: x[97]:=-x[3]: y[97]:=y[3]: z[97]:=-z[3]: x[98]:=-x[3]: y[98]:=y[4]: z[98]:=-z[3]: x[99]:=-x[2]: y[99]:=-y[2]: z[99]:=-z[2]: x[100]:=-x[1]: y[100]:=-y[1]: z[100]:=-z[1]: x[101]:=-x[12]: y[101]:=y[12]: z[101]:=z[12]: x[102]:=-x[11]: y[102]:=y[11]: z[102]:=z[11]: x[103]:=-x[19]: y[103]:=y[19]: z[103]:=z[20]: x[104]:=-x[19]: y[104]:=y[19]: z[104]:=z[19]: x[105]:=-x[11]: y[105]:=y[11]: z[105]:=-z[11]: x[106]:=-x[12]: y[106]:=y[12]: z[106]:=-z[12]: x[107]:=-x[13]: y[107]:=y[13]: z[107]:=-z[13]: x[108]:=-x[14]: y[108]:=y[14]: z[108]:=-z[14]: x[109]:=-x[14]: y[109]:=y[14]: z[109]:=z[14]: x[110]:=-x[13]: y[110]:=y[13]: z[110]:=z[13]: x[111]:=-x[8]: y[111]:=-y[8]: z[111]:=z[8]: x[112]:=-x[8]: y[112]:=y[8]: z[112]:=z[8]: x[113]:=-y[11]: y[113]:=-z[11]: z[113]:=x[11]: x[114]:=-y[12]: y[114]:=-z[12]: z[114]:=x[12]: x[115]:=-y[13]: y[115]:=-z[13]: z[115]:=x[13]: x[116]:=-y[14]: y[116]:=-z[14]: z[116]:=x[14]: x[117]:=-y[14]: y[117]:=z[14]: z[117]:=x[14]: x[118]:=-y[13]: y[118]:=z[13]: z[118]:=x[13]: x[119]:=-y[12]: y[119]:=z[12]: z[119]:=x[12]: x[120]:=-y[11]: y[120]:=z[11]: z[120]:=x[11]:

> for i from 1 to 120 do a[i]:=[x[i],y[i],z[i]] od:

> for i from 1 to 12 do g[i]:=[seq(a[10*i-10+j],j=1..10)] od:

> g[13]:=[a[1],a[29],a[28],a[2]]: g[14]:=[a[3],a[117],a[116],a[4]]: g[15]:=[a[5],a[75],a[74],a[6]]: g[16]:=[a[7],a[57],a[56],a[8]]: g[17]:=[a[9],a[13],a[12],a[10]]: g[18]:=[a[14],a[55],a[54],a[15]]: g[19]:=[a[16],a[45],a[44],a[17]]: g[20]:=[a[18],a[38],a[37],a[19]]: g[21]:=[a[11],a[20],a[21],a[30]]: g[22]:=[a[22],a[36],a[35],a[23]]: g[23]:=[a[24],a[103],a[102],a[25]]: g[24]:=[a[26],a[119],a[118],a[27]]: g[25]:=[a[58],a[73],a[72],a[59]]: g[26]:=[a[51],a[60],a[69],a[68]]: g[27]:=[a[52],a[47],a[46],a[53]]: g[28]:=[a[48],a[67],a[66],a[49]]: g[29]:=[a[41],a[50],a[98],a[97]]: g[30]:=[a[42],a[40],a[39],a[43]]: g[31]:=[a[31],a[96],a[95],a[32]]: g[32]:=[a[33],a[105],a[104],a[34]]: g[33]:=[a[61],a[70],a[71],a[80]]: g[34]:=[a[62],a[82],a[81],a[63]]: g[35]:=[a[64],a[100],a[99],a[65]]: g[36]:=[a[76],a[115],a[114],a[77]]: g[37]:=[a[78],a[84],a[83],a[79]]: g[38]:=[a[85],a[113],a[112],a[86]]: g[39]:=[a[87],a[109],a[108],a[88]]: g[40]:=[a[90],a[89],a[92],a[91]]: g[41]:=[a[93],a[107],a[106],a[94]]: g[42]:=[a[101],a[110],a[111],a[120]]: g[43]:=[a[1],a[10],a[12],a[11],a[30],a[29]]: g[44]:=[a[8],a[56],a[55],a[14],a[13],a[9]]: g[45]:=[a[6],a[74],a[73],a[58],a[57],a[7]]: g[46]:=[a[4],a[116],a[115],a[76],a[75],a[5]]: g[47]:=[a[2],a[28],a[27],a[118],a[117],a[3]]: g[48]:=[a[15],a[54],a[53],a[46],a[45],a[16]]: g[49]:=[a[17],a[44],a[43],a[39],a[38],a[18]]: g[50]:=[a[19],a[37],a[36],a[22],a[21],a[20]]: g[51]:=[a[23],a[35],a[34],a[104],a[103],a[24]]: g[52]:=[a[25],a[102],a[101],a[120],a[119],a[26]]: g[53]:=[a[32],a[95],a[94],a[106],a[105],a[33]]: g[54]:=[a[31],a[40],a[42],a[41],a[97],a[96]]: g[55]:=[a[47],a[52],a[51],a[68],a[67],a[48]]: g[56]:=[a[49],a[66],a[65],a[99],a[98],a[50]]: g[57]:=[a[59],a[72],a[71],a[70],a[69],a[60]]: g[58]:=[a[61],a[80],a[79],a[83],a[82],a[62]]: g[59]:=[a[63],a[81],a[90],a[91],a[100],a[64]]: g[60]:=[a[77],a[114],a[113],a[85],a[84],a[78]]: g[61]:=[a[86],a[112],a[111],a[110],a[109],a[87]]: g[62]:=[a[88],a[108],a[107],a[93],a[92],a[89]]:

> P:=j -> plots[polygonplot3d]([seq(g[i], i=1..62)], orientation=[20*j,50], style=PATCH):

> plots[display]([seq(P(j), j=1..18)], insequence=true, scaling=constrained);

> plots[display](plottools[stellate](POLYGONS(seq(g[i],i=1..62))), style=patch, lightmodel=light2, scaling=constrained);

3444-2 (Ashkinuze)

> restart: # 3444-2

> c:=1: d:=evalf((c*sqrt(2))/(2+sqrt(2))):

> x[1]:=d: y[1]:=d: z[1]:=c: x[2]:=-d: y[2]:=d: z[2]:=c: x[3]:=-d: y[3]:=-d: z[3]:=c: x[4]:=d: y[4]:=-d: z[4]:=c: x[5]:=c: y[5]:=d: z[5]:=d: x[6]:=c: y[6]:=d: z[6]:=-d: x[7]:=c: y[7]:=-d: z[7]:=-d: x[8]:=c: y[8]:=-d: z[8]:=d: x[9]:=-d: y[9]:=c: z[9]:=d: x[10]:=-d: y[10]:=c: z[10]:=-d: x[11]:=d:y[11]:=c:z[11]:=-d: x[12]:=d:y[12]:=c:z[12]:=d: x[13]:=d:y[13]:=-c:z[13]:=d: x[14]:=d:y[14]:=-c:z[14]:=-d: x[15]:=-d:y[15]:=-c: z[15]:=-d: x[16]:=-d :y[16]:=-c :z[16]:=d: x[17]:=-c :y[17]:=-d :z[17]:=d :x[18]:=-c: y[18]:=-d: z[18]:=-d: x[19]:=-c:y[19]:=d:z[19]:=-d: x[20]:=-c:y[20]:=d:z[20]:=d: x[21]:=evalf(d*sqrt(2)): y[21]:=0: z[21]:=-c: x[22]:=0: y[22]:=evalf(d*sqrt(2)): z[22]:=-c: x[23]:=evalf(-d*sqrt(2)): y[23]:=0: z[23]:=-c: x[24]:=0: y[24]:=evalf(-d*sqrt(2)): z[24]:=-c:

> for i from 1 to 24 do a[i]:=[x[i],y[i],z[i]] od:

> for i from 1 to 6 do g[i]:=[seq(a[4*(i-1)+j],j=1..4)] od:

> g[7]:=[a[1],a[4],a[8],a[5]]: g[8]:=[a[4],a[13],a[16],a[3]]: g[9]:=[a[3],a[17],a[20],a[2]]: g[10]:=[a[2],a[9],a[12],a[1]]: g[11]:=[a[12],a[5],a[6],a[11]]: g[12]:=[a[8],a[13],a[14],a[7]]: g[13]:=[a[16],a[17],a[18],a[15]]: g[14]:=[a[20],a[9],a[10],a[19]]:g[15]:=[a[11],a[22],a[21],a[6]]: g[16]:=[a[7],a[21],a[24],a[14]]: g[17]:=[a[15],a[24],a[23],a[18]]: g[18]:=[a[10],a[19],a[23],a[22]]: g[19]:=[a[1],a[12],a[5]]: g[20]:=[a[4],a[8],a[13]]: g[21]:=[a[3],a[16],a[17]]: g[22]:=[a[2],a[20],a[9]]: g[23]:=[a[6],a[21],a[7]]: g[24]:=[a[14],a[24],a[15]]: g[25]:=[a[18],a[23],a[19]]: g[26]:=[a[10],a[22],a[11]]:

> P:=j -> plots[polygonplot3d]([seq(g[i], i=1..26)], orientation=[20*j,50], style=PATCH):

> plots[display]([seq(P(j), j=1..18)], insequence=true, scaling=constrained);

> plots[display](plottools[stellate](POLYGONS(seq(g[i],i=1..26))), style=patch, lightmodel=light2, scaling=constrained);

33n

> restart: # 333n

> n:=9: r:=1: u:=evalf(Pi/n): c:=evalf((r*sqrt(3*sqrt(sin(Pi/n))-sqrt(1-cos(Pi/n))))/2):

> for i from 1 to n+1 do x[2*i-1]:= evalf(r*cos(i*2*Pi/n)): y[2*i-1]:=evalf(r*sin(i*2*Pi/n)): z[2*i-1]:=c: x[2*i]:=evalf(r*cos(u+i*2*Pi/n)): y[2*i]:=evalf(r*sin(u+i*2*Pi/n)): z[2*i]:=-z[2*i-1] od:

> for i from 1 to 2*n+2 do a[i]:=[x[i],y[i],z[i]] od:

> for i from 1 to 2*n do g[i]:=[a[i], a[i+1], a[i+2]] od: g[2*n+2]:=[seq(a[2*i], i=1..n)]: g[2*n+1]:=[seq(a[2*i-1], i=1..n)]:

> P:=j -> plots[polygonplot3d]([seq(g[i], i=1..2*n+2)], orientation=[20*j, 50], style=PATCH):

> plots[display]([seq(P(j), j=1..18)], insequence=true, scaling=constrained);

> plots[display](plottools[stellate](POLYGONS(seq(g[i],i=1..2*n+2))), style=patch, lightmodel=light2, scaling=constrained);

44n

> restart: # 44n

> n:=7: r:=1: c:=evalf(r*sin(Pi/n)): # n-prism

> a:=i->[evalf(r*cos(i*2*Pi/n)), evalf(r*sin(i*2*Pi/n)),0]:

> for i from 1 to n do g[i]:=[a(i),a(i+1),a(i+1)+[0,0,2*c],a(i)+[0,0,2*c]] od: g[n+1]:=[seq(a(i), i=1..n)]: g[n+2]:=[seq(a(i)+[0,0,2*c], i=1..n)]:

> P:=j -> plots[polygonplot3d]([seq(g[i], i=1..n+2)], orientation=[20*j,50], style=PATCH):

> plots[display]([seq(P(j), j=1..18)], insequence=true);

>