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Polytope of Type {76}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {76}*152
Also Known As : 76-gon, {76}. if this polytope has another name.
Group : SmallGroup(152,5)
Rank : 2
Schlafli Type : {76}
Number of vertices, edges, etc : 76, 76
Order of s₀s₁ : 76
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {76,2} of size 304
   {76,4} of size 608
   {76,6} of size 912
   {76,6} of size 912
   {76,8} of size 1216
   {76,8} of size 1216
   {76,4} of size 1216
   {76,6} of size 1368
   {76,10} of size 1520
   {76,12} of size 1824
   {76,6} of size 1824
Vertex Figure Of :
   {2,76} of size 304
   {4,76} of size 608
   {6,76} of size 912
   {6,76} of size 912
   {8,76} of size 1216
   {8,76} of size 1216
   {4,76} of size 1216
   {6,76} of size 1368
   {10,76} of size 1520
   {12,76} of size 1824
   {6,76} of size 1824
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {38}*76
   4-fold quotients : {19}*38
   19-fold quotients : {4}*8
   38-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {152}*304
   3-fold covers : {228}*456
   4-fold covers : {304}*608
   5-fold covers : {380}*760
   6-fold covers : {456}*912
   7-fold covers : {532}*1064
   8-fold covers : {608}*1216
   9-fold covers : {684}*1368
   10-fold covers : {760}*1520
   11-fold covers : {836}*1672
   12-fold covers : {912}*1824
   13-fold covers : {988}*1976
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)(39,58)(40,76)(41,75)
(42,74)(43,73)(44,72)(45,71)(46,70)(47,69)(48,68)(49,67)(50,66)(51,65)(52,64)
(53,63)(54,62)(55,61)(56,60)(57,59);;
s1 := ( 1,40)( 2,39)( 3,57)( 4,56)( 5,55)( 6,54)( 7,53)( 8,52)( 9,51)(10,50)
(11,49)(12,48)(13,47)(14,46)(15,45)(16,44)(17,43)(18,42)(19,41)(20,59)(21,58)
(22,76)(23,75)(24,74)(25,73)(26,72)(27,71)(28,70)(29,69)(30,68)(31,67)(32,66)
(33,65)(34,64)(35,63)(36,62)(37,61)(38,60);;
poly := Group([s0,s1]);;

Finitely Presented Group Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1> := Group< s0,s1 | s0*s0, s1*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*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*s0*s1 >;

References : None.
to this polytope