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# Polytope of Type {8,16}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,16}*256a
if this polytope has a name.
Group : SmallGroup(256,5298)
Rank : 3
Schlafli Type : {8,16}
Number of vertices, edges, etc : 8, 64, 16
Order of s0s1s2 : 16
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{8,16,2} of size 512
Vertex Figure Of :
{2,8,16} of size 512
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {8,8}*128c
4-fold quotients : {8,4}*64a, {4,8}*64b
8-fold quotients : {4,4}*32, {8,2}*32
16-fold quotients : {2,4}*16, {4,2}*16
32-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {16,16}*512c, {16,16}*512f, {8,16}*512f
3-fold covers : {8,48}*768a, {24,16}*768a
5-fold covers : {8,80}*1280a, {40,16}*1280a
7-fold covers : {8,112}*1792a, {56,16}*1792a
Permutation Representation (GAP) :
```s0 := ( 1,33)( 2,34)( 3,36)( 4,35)( 5,39)( 6,40)( 7,37)( 8,38)( 9,41)(10,42)
(11,44)(12,43)(13,47)(14,48)(15,45)(16,46)(17,49)(18,50)(19,52)(20,51)(21,55)
(22,56)(23,53)(24,54)(25,58)(26,57)(27,59)(28,60)(29,64)(30,63)(31,62)
(32,61);;
s1 := ( 3, 4)( 5, 7)( 6, 8)(11,12)(13,15)(14,16)(17,21)(18,22)(19,24)(20,23)
(25,30)(26,29)(27,31)(28,32)(33,41)(34,42)(35,44)(36,43)(37,47)(38,48)(39,45)
(40,46)(49,63)(50,64)(51,61)(52,62)(53,59)(54,60)(55,57)(56,58);;
s2 := ( 1,17)( 2,18)( 3,20)( 4,19)( 5,23)( 6,24)( 7,21)( 8,22)( 9,27)(10,28)
(11,25)(12,26)(13,30)(14,29)(15,31)(16,32)(33,49)(34,50)(35,52)(36,51)(37,55)
(38,56)(39,53)(40,54)(41,59)(42,60)(43,57)(44,58)(45,62)(46,61)(47,63)
(48,64);;
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*s1*s2*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope