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# Polytope of Type {8,8}

Atlas Canonical Name : {8,8}*128d
if this polytope has a name.
Group : SmallGroup(128,387)
Rank : 3
Schlafli Type : {8,8}
Number of vertices, edges, etc : 8, 32, 8
Order of s0s1s2 : 8
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Dual
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{8,8,2} of size 256
{8,8,4} of size 512
{8,8,4} of size 512
{8,8,6} of size 768
{8,8,10} of size 1280
{8,8,14} of size 1792
Vertex Figure Of :
{2,8,8} of size 256
{4,8,8} of size 512
{4,8,8} of size 512
{6,8,8} of size 768
{10,8,8} of size 1280
{14,8,8} of size 1792
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,8}*64b, {8,4}*64b
4-fold quotients : {4,4}*32
8-fold quotients : {2,4}*16, {4,2}*16
16-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {8,8}*256a
3-fold covers : {8,24}*384c, {24,8}*384c
4-fold covers : {8,16}*512c, {16,8}*512c, {8,16}*512d, {16,8}*512d, {8,16}*512e, {16,8}*512e, {8,16}*512f, {16,8}*512f, {8,8}*512a, {8,8}*512b, {8,8}*512c
5-fold covers : {8,40}*640c, {40,8}*640c
6-fold covers : {8,24}*768a, {24,8}*768a
7-fold covers : {8,56}*896c, {56,8}*896c
9-fold covers : {8,72}*1152d, {72,8}*1152d, {24,24}*1152j, {24,24}*1152k, {24,24}*1152l, {8,8}*1152d, {8,24}*1152d, {24,8}*1152d
10-fold covers : {8,40}*1280a, {40,8}*1280a
11-fold covers : {8,88}*1408d, {88,8}*1408d
13-fold covers : {8,104}*1664d, {104,8}*1664d
14-fold covers : {8,56}*1792a, {56,8}*1792a
15-fold covers : {8,120}*1920d, {120,8}*1920d, {24,40}*1920d, {40,24}*1920d
Permutation Representation (GAP) :
```s0 := ( 1,17)( 2,18)( 3,19)( 4,20)( 5,24)( 6,23)( 7,22)( 8,21)( 9,26)(10,25)
(11,28)(12,27)(13,31)(14,32)(15,29)(16,30)(33,49)(34,50)(35,51)(36,52)(37,56)
(38,55)(39,54)(40,53)(41,58)(42,57)(43,60)(44,59)(45,63)(46,64)(47,61)
(48,62);;
s1 := ( 5, 8)( 6, 7)( 9,11)(10,12)(13,14)(15,16)(17,21)(18,22)(19,23)(20,24)
(25,31)(26,32)(27,29)(28,30)(33,41)(34,42)(35,43)(36,44)(37,48)(38,47)(39,46)
(40,45)(49,62)(50,61)(51,64)(52,63)(53,58)(54,57)(55,60)(56,59);;
s2 := ( 1,33)( 2,34)( 3,35)( 4,36)( 5,38)( 6,37)( 7,40)( 8,39)( 9,43)(10,44)
(11,41)(12,42)(13,48)(14,47)(15,46)(16,45)(17,49)(18,50)(19,51)(20,52)(21,54)
(22,53)(23,56)(24,55)(25,59)(26,60)(27,57)(28,58)(29,64)(30,63)(31,62)
(32,61);;
poly := Group([s0,s1,s2]);;

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

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

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

```
References : None.
to this polytope