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Polytope of Type {74,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {74,2}*296
if this polytope has a name.
Group : SmallGroup(296,13)
Rank : 3
Schlafli Type : {74,2}
Number of vertices, edges, etc : 74, 74, 2
Order of s0s1s2 : 74
Order of s0s1s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {74,2,2} of size 592
   {74,2,3} of size 888
   {74,2,4} of size 1184
   {74,2,5} of size 1480
   {74,2,6} of size 1776
Vertex Figure Of :
   {2,74,2} of size 592
   {4,74,2} of size 1184
   {6,74,2} of size 1776
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {37,2}*148
   37-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {148,2}*592, {74,4}*592
   3-fold covers : {74,6}*888, {222,2}*888
   4-fold covers : {148,4}*1184, {74,8}*1184, {296,2}*1184
   5-fold covers : {74,10}*1480, {370,2}*1480
   6-fold covers : {74,12}*1776, {148,6}*1776a, {444,2}*1776, {222,4}*1776a
Permutation Representation (GAP) :
s0 := ( 2,37)( 3,36)( 4,35)( 5,34)( 6,33)( 7,32)( 8,31)( 9,30)(10,29)(11,28)
(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)(39,74)(40,73)(41,72)
(42,71)(43,70)(44,69)(45,68)(46,67)(47,66)(48,65)(49,64)(50,63)(51,62)(52,61)
(53,60)(54,59)(55,58)(56,57);;
s1 := ( 1,39)( 2,38)( 3,74)( 4,73)( 5,72)( 6,71)( 7,70)( 8,69)( 9,68)(10,67)
(11,66)(12,65)(13,64)(14,63)(15,62)(16,61)(17,60)(18,59)(19,58)(20,57)(21,56)
(22,55)(23,54)(24,53)(25,52)(26,51)(27,50)(28,49)(29,48)(30,47)(31,46)(32,45)
(33,44)(34,43)(35,42)(36,41)(37,40);;
s2 := (75,76);;
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, 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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)!( 2,37)( 3,36)( 4,35)( 5,34)( 6,33)( 7,32)( 8,31)( 9,30)(10,29)
(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)(39,74)(40,73)
(41,72)(42,71)(43,70)(44,69)(45,68)(46,67)(47,66)(48,65)(49,64)(50,63)(51,62)
(52,61)(53,60)(54,59)(55,58)(56,57);
s1 := Sym(76)!( 1,39)( 2,38)( 3,74)( 4,73)( 5,72)( 6,71)( 7,70)( 8,69)( 9,68)
(10,67)(11,66)(12,65)(13,64)(14,63)(15,62)(16,61)(17,60)(18,59)(19,58)(20,57)
(21,56)(22,55)(23,54)(24,53)(25,52)(26,51)(27,50)(28,49)(29,48)(30,47)(31,46)
(32,45)(33,44)(34,43)(35,42)(36,41)(37,40);
s2 := Sym(76)!(75,76);
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, 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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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