# Polytope of Type {38,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {38,4}*304
Also Known As : {38,4|2}. if this polytope has another name.
Group : SmallGroup(304,31)
Rank : 3
Schlafli Type : {38,4}
Number of vertices, edges, etc : 38, 76, 4
Order of s0s1s2 : 76
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{38,4,2} of size 608
{38,4,4} of size 1216
{38,4,6} of size 1824
{38,4,3} of size 1824
Vertex Figure Of :
{2,38,4} of size 608
{4,38,4} of size 1216
{6,38,4} of size 1824
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {38,2}*152
4-fold quotients : {19,2}*76
19-fold quotients : {2,4}*16
38-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {76,4}*608, {38,8}*608
3-fold covers : {38,12}*912, {114,4}*912a
4-fold covers : {76,8}*1216a, {152,4}*1216a, {76,8}*1216b, {152,4}*1216b, {76,4}*1216, {38,16}*1216
5-fold covers : {38,20}*1520, {190,4}*1520
6-fold covers : {38,24}*1824, {76,12}*1824, {228,4}*1824a, {114,8}*1824
Permutation Representation (GAP) :
```s0 := ( 2,19)( 3,18)( 4,17)( 5,16)( 6,15)( 7,14)( 8,13)( 9,12)(10,11)(21,38)
(22,37)(23,36)(24,35)(25,34)(26,33)(27,32)(28,31)(29,30)(40,57)(41,56)(42,55)
(43,54)(44,53)(45,52)(46,51)(47,50)(48,49)(59,76)(60,75)(61,74)(62,73)(63,72)
(64,71)(65,70)(66,69)(67,68);;
s1 := ( 1, 2)( 3,19)( 4,18)( 5,17)( 6,16)( 7,15)( 8,14)( 9,13)(10,12)(20,21)
(22,38)(23,37)(24,36)(25,35)(26,34)(27,33)(28,32)(29,31)(39,59)(40,58)(41,76)
(42,75)(43,74)(44,73)(45,72)(46,71)(47,70)(48,69)(49,68)(50,67)(51,66)(52,65)
(53,64)(54,63)(55,62)(56,61)(57,60);;
s2 := ( 1,39)( 2,40)( 3,41)( 4,42)( 5,43)( 6,44)( 7,45)( 8,46)( 9,47)(10,48)
(11,49)(12,50)(13,51)(14,52)(15,53)(16,54)(17,55)(18,56)(19,57)(20,58)(21,59)
(22,60)(23,61)(24,62)(25,63)(26,64)(27,65)(28,66)(29,67)(30,68)(31,69)(32,70)
(33,71)(34,72)(35,73)(36,74)(37,75)(38,76);;
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, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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(76)!( 2,19)( 3,18)( 4,17)( 5,16)( 6,15)( 7,14)( 8,13)( 9,12)(10,11)
(21,38)(22,37)(23,36)(24,35)(25,34)(26,33)(27,32)(28,31)(29,30)(40,57)(41,56)
(42,55)(43,54)(44,53)(45,52)(46,51)(47,50)(48,49)(59,76)(60,75)(61,74)(62,73)
(63,72)(64,71)(65,70)(66,69)(67,68);
s1 := Sym(76)!( 1, 2)( 3,19)( 4,18)( 5,17)( 6,16)( 7,15)( 8,14)( 9,13)(10,12)
(20,21)(22,38)(23,37)(24,36)(25,35)(26,34)(27,33)(28,32)(29,31)(39,59)(40,58)
(41,76)(42,75)(43,74)(44,73)(45,72)(46,71)(47,70)(48,69)(49,68)(50,67)(51,66)
(52,65)(53,64)(54,63)(55,62)(56,61)(57,60);
s2 := Sym(76)!( 1,39)( 2,40)( 3,41)( 4,42)( 5,43)( 6,44)( 7,45)( 8,46)( 9,47)
(10,48)(11,49)(12,50)(13,51)(14,52)(15,53)(16,54)(17,55)(18,56)(19,57)(20,58)
(21,59)(22,60)(23,61)(24,62)(25,63)(26,64)(27,65)(28,66)(29,67)(30,68)(31,69)
(32,70)(33,71)(34,72)(35,73)(36,74)(37,75)(38,76);
poly := sub<Sym(76)|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, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

```
References : None.
to this polytope