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.
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