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Polytope of Type {74}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {74}*148
Also Known As : 74-gon, {74}. if this polytope has another name.
Group : SmallGroup(148,4)
Rank : 2
Schlafli Type : {74}
Number of vertices, edges, etc : 74, 74
Order of s0s1 : 74
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {74,2} of size 296
   {74,4} of size 592
   {74,6} of size 888
   {74,8} of size 1184
   {74,10} of size 1480
   {74,12} of size 1776
Vertex Figure Of :
   {2,74} of size 296
   {4,74} of size 592
   {6,74} of size 888
   {8,74} of size 1184
   {10,74} of size 1480
   {12,74} of size 1776
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {37}*74
   37-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {148}*296
   3-fold covers : {222}*444
   4-fold covers : {296}*592
   5-fold covers : {370}*740
   6-fold covers : {444}*888
   7-fold covers : {518}*1036
   8-fold covers : {592}*1184
   9-fold covers : {666}*1332
   10-fold covers : {740}*1480
   11-fold covers : {814}*1628
   12-fold covers : {888}*1776
   13-fold covers : {962}*1924
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);;
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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(74)!( 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(74)!( 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);
poly := sub<Sym(74)|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 >; 
 
References : None.
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