# Polytope of Type {2,8,8}

Atlas Canonical Name : {2,8,8}*256c
if this polytope has a name.
Group : SmallGroup(256,11462)
Rank : 4
Schlafli Type : {2,8,8}
Number of vertices, edges, etc : 2, 8, 32, 8
Order of s0s1s2s3 : 8
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,8,8,2} of size 512
Vertex Figure Of :
{2,2,8,8} of size 512
{3,2,8,8} of size 768
{5,2,8,8} of size 1280
{7,2,8,8} of size 1792
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,8,4}*128a, {2,4,8}*128b
4-fold quotients : {2,4,4}*64, {2,8,2}*64
8-fold quotients : {2,2,4}*32, {2,4,2}*32
16-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,8,8}*512a, {4,8,8}*512f, {2,8,16}*512a, {2,8,16}*512b, {2,16,8}*512c, {2,16,8}*512e
3-fold covers : {6,8,8}*768c, {2,8,24}*768a, {2,24,8}*768b
5-fold covers : {10,8,8}*1280c, {2,8,40}*1280a, {2,40,8}*1280b
7-fold covers : {14,8,8}*1792c, {2,8,56}*1792a, {2,56,8}*1792b
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 3,35)( 4,36)( 5,37)( 6,38)( 7,40)( 8,39)( 9,42)(10,41)(11,45)(12,46)
(13,43)(14,44)(15,50)(16,49)(17,48)(18,47)(19,51)(20,52)(21,53)(22,54)(23,56)
(24,55)(25,58)(26,57)(27,61)(28,62)(29,59)(30,60)(31,66)(32,65)(33,64)
(34,63);;
s2 := ( 7, 8)( 9,10)(11,13)(12,14)(15,18)(16,17)(19,23)(20,24)(21,25)(22,26)
(27,33)(28,34)(29,31)(30,32)(35,43)(36,44)(37,45)(38,46)(39,48)(40,47)(41,50)
(42,49)(51,64)(52,63)(53,66)(54,65)(55,60)(56,59)(57,62)(58,61);;
s3 := ( 3,19)( 4,20)( 5,21)( 6,22)( 7,24)( 8,23)( 9,26)(10,25)(11,28)(12,27)
(13,30)(14,29)(15,31)(16,32)(17,33)(18,34)(35,51)(36,52)(37,53)(38,54)(39,56)
(40,55)(41,58)(42,57)(43,60)(44,59)(45,62)(46,61)(47,63)(48,64)(49,65)
(50,66);;
poly := Group([s0,s1,s2,s3]);;

```
Finitely Presented Group Representation (GAP) :
```F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(66)!(1,2);
s1 := Sym(66)!( 3,35)( 4,36)( 5,37)( 6,38)( 7,40)( 8,39)( 9,42)(10,41)(11,45)
(12,46)(13,43)(14,44)(15,50)(16,49)(17,48)(18,47)(19,51)(20,52)(21,53)(22,54)
(23,56)(24,55)(25,58)(26,57)(27,61)(28,62)(29,59)(30,60)(31,66)(32,65)(33,64)
(34,63);
s2 := Sym(66)!( 7, 8)( 9,10)(11,13)(12,14)(15,18)(16,17)(19,23)(20,24)(21,25)
(22,26)(27,33)(28,34)(29,31)(30,32)(35,43)(36,44)(37,45)(38,46)(39,48)(40,47)
(41,50)(42,49)(51,64)(52,63)(53,66)(54,65)(55,60)(56,59)(57,62)(58,61);
s3 := Sym(66)!( 3,19)( 4,20)( 5,21)( 6,22)( 7,24)( 8,23)( 9,26)(10,25)(11,28)
(12,27)(13,30)(14,29)(15,31)(16,32)(17,33)(18,34)(35,51)(36,52)(37,53)(38,54)
(39,56)(40,55)(41,58)(42,57)(43,60)(44,59)(45,62)(46,61)(47,63)(48,64)(49,65)
(50,66);
poly := sub<Sym(66)|s0,s1,s2,s3>;

```
Finitely Presented Group Representation (Magma) :
```poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2 >;

```

to this polytope