# Polytope of Type {2,76}

Atlas Canonical Name : {2,76}*304
if this polytope has a name.
Group : SmallGroup(304,29)
Rank : 3
Schlafli Type : {2,76}
Number of vertices, edges, etc : 2, 76, 76
Order of s0s1s2 : 76
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,76,2} of size 608
{2,76,4} of size 1216
{2,76,6} of size 1824
{2,76,6} of size 1824
Vertex Figure Of :
{2,2,76} of size 608
{3,2,76} of size 912
{4,2,76} of size 1216
{5,2,76} of size 1520
{6,2,76} of size 1824
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,38}*152
4-fold quotients : {2,19}*76
19-fold quotients : {2,4}*16
38-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,76}*608, {2,152}*608
3-fold covers : {6,76}*912a, {2,228}*912
4-fold covers : {8,76}*1216a, {4,152}*1216a, {8,76}*1216b, {4,152}*1216b, {4,76}*1216, {2,304}*1216
5-fold covers : {10,76}*1520, {2,380}*1520
6-fold covers : {6,152}*1824, {12,76}*1824, {4,228}*1824a, {2,456}*1824
Permutation Representation (GAP) :
```s0 := (1,2);;
s1 := ( 4,21)( 5,20)( 6,19)( 7,18)( 8,17)( 9,16)(10,15)(11,14)(12,13)(23,40)
(24,39)(25,38)(26,37)(27,36)(28,35)(29,34)(30,33)(31,32)(41,60)(42,78)(43,77)
(44,76)(45,75)(46,74)(47,73)(48,72)(49,71)(50,70)(51,69)(52,68)(53,67)(54,66)
(55,65)(56,64)(57,63)(58,62)(59,61);;
s2 := ( 3,42)( 4,41)( 5,59)( 6,58)( 7,57)( 8,56)( 9,55)(10,54)(11,53)(12,52)
(13,51)(14,50)(15,49)(16,48)(17,47)(18,46)(19,45)(20,44)(21,43)(22,61)(23,60)
(24,78)(25,77)(26,76)(27,75)(28,74)(29,73)(30,72)(31,71)(32,70)(33,69)(34,68)
(35,67)(36,66)(37,65)(38,64)(39,63)(40,62);;
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*s1*s0*s1, s0*s2*s0*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(78)!(1,2);
s1 := Sym(78)!( 4,21)( 5,20)( 6,19)( 7,18)( 8,17)( 9,16)(10,15)(11,14)(12,13)
(23,40)(24,39)(25,38)(26,37)(27,36)(28,35)(29,34)(30,33)(31,32)(41,60)(42,78)
(43,77)(44,76)(45,75)(46,74)(47,73)(48,72)(49,71)(50,70)(51,69)(52,68)(53,67)
(54,66)(55,65)(56,64)(57,63)(58,62)(59,61);
s2 := Sym(78)!( 3,42)( 4,41)( 5,59)( 6,58)( 7,57)( 8,56)( 9,55)(10,54)(11,53)
(12,52)(13,51)(14,50)(15,49)(16,48)(17,47)(18,46)(19,45)(20,44)(21,43)(22,61)
(23,60)(24,78)(25,77)(26,76)(27,75)(28,74)(29,73)(30,72)(31,71)(32,70)(33,69)
(34,68)(35,67)(36,66)(37,65)(38,64)(39,63)(40,62);
poly := sub<Sym(78)|s0,s1,s2>;

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

```

to this polytope