Polytope of Type {124}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {124}*248
Also Known As : 124-gon, {124}. if this polytope has another name.
Group : SmallGroup(248,5)
Rank : 2
Schlafli Type : {124}
Number of vertices, edges, etc : 124, 124
Order of s0s1 : 124
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {124,2} of size 496
   {124,4} of size 992
   {124,6} of size 1488
   {124,6} of size 1488
   {124,8} of size 1984
   {124,8} of size 1984
   {124,4} of size 1984
Vertex Figure Of :
   {2,124} of size 496
   {4,124} of size 992
   {6,124} of size 1488
   {6,124} of size 1488
   {8,124} of size 1984
   {8,124} of size 1984
   {4,124} of size 1984
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {62}*124
   4-fold quotients : {31}*62
   31-fold quotients : {4}*8
   62-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {248}*496
   3-fold covers : {372}*744
   4-fold covers : {496}*992
   5-fold covers : {620}*1240
   6-fold covers : {744}*1488
   7-fold covers : {868}*1736
   8-fold covers : {992}*1984
Permutation Representation (GAP) :
s0 := (  2, 31)(  3, 30)(  4, 29)(  5, 28)(  6, 27)(  7, 26)(  8, 25)(  9, 24)
( 10, 23)( 11, 22)( 12, 21)( 13, 20)( 14, 19)( 15, 18)( 16, 17)( 33, 62)
( 34, 61)( 35, 60)( 36, 59)( 37, 58)( 38, 57)( 39, 56)( 40, 55)( 41, 54)
( 42, 53)( 43, 52)( 44, 51)( 45, 50)( 46, 49)( 47, 48)( 63, 94)( 64,124)
( 65,123)( 66,122)( 67,121)( 68,120)( 69,119)( 70,118)( 71,117)( 72,116)
( 73,115)( 74,114)( 75,113)( 76,112)( 77,111)( 78,110)( 79,109)( 80,108)
( 81,107)( 82,106)( 83,105)( 84,104)( 85,103)( 86,102)( 87,101)( 88,100)
( 89, 99)( 90, 98)( 91, 97)( 92, 96)( 93, 95);;
s1 := (  1, 64)(  2, 63)(  3, 93)(  4, 92)(  5, 91)(  6, 90)(  7, 89)(  8, 88)
(  9, 87)( 10, 86)( 11, 85)( 12, 84)( 13, 83)( 14, 82)( 15, 81)( 16, 80)
( 17, 79)( 18, 78)( 19, 77)( 20, 76)( 21, 75)( 22, 74)( 23, 73)( 24, 72)
( 25, 71)( 26, 70)( 27, 69)( 28, 68)( 29, 67)( 30, 66)( 31, 65)( 32, 95)
( 33, 94)( 34,124)( 35,123)( 36,122)( 37,121)( 38,120)( 39,119)( 40,118)
( 41,117)( 42,116)( 43,115)( 44,114)( 45,113)( 46,112)( 47,111)( 48,110)
( 49,109)( 50,108)( 51,107)( 52,106)( 53,105)( 54,104)( 55,103)( 56,102)
( 57,101)( 58,100)( 59, 99)( 60, 98)( 61, 97)( 62, 96);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(124)!(  2, 31)(  3, 30)(  4, 29)(  5, 28)(  6, 27)(  7, 26)(  8, 25)
(  9, 24)( 10, 23)( 11, 22)( 12, 21)( 13, 20)( 14, 19)( 15, 18)( 16, 17)
( 33, 62)( 34, 61)( 35, 60)( 36, 59)( 37, 58)( 38, 57)( 39, 56)( 40, 55)
( 41, 54)( 42, 53)( 43, 52)( 44, 51)( 45, 50)( 46, 49)( 47, 48)( 63, 94)
( 64,124)( 65,123)( 66,122)( 67,121)( 68,120)( 69,119)( 70,118)( 71,117)
( 72,116)( 73,115)( 74,114)( 75,113)( 76,112)( 77,111)( 78,110)( 79,109)
( 80,108)( 81,107)( 82,106)( 83,105)( 84,104)( 85,103)( 86,102)( 87,101)
( 88,100)( 89, 99)( 90, 98)( 91, 97)( 92, 96)( 93, 95);
s1 := Sym(124)!(  1, 64)(  2, 63)(  3, 93)(  4, 92)(  5, 91)(  6, 90)(  7, 89)
(  8, 88)(  9, 87)( 10, 86)( 11, 85)( 12, 84)( 13, 83)( 14, 82)( 15, 81)
( 16, 80)( 17, 79)( 18, 78)( 19, 77)( 20, 76)( 21, 75)( 22, 74)( 23, 73)
( 24, 72)( 25, 71)( 26, 70)( 27, 69)( 28, 68)( 29, 67)( 30, 66)( 31, 65)
( 32, 95)( 33, 94)( 34,124)( 35,123)( 36,122)( 37,121)( 38,120)( 39,119)
( 40,118)( 41,117)( 42,116)( 43,115)( 44,114)( 45,113)( 46,112)( 47,111)
( 48,110)( 49,109)( 50,108)( 51,107)( 52,106)( 53,105)( 54,104)( 55,103)
( 56,102)( 57,101)( 58,100)( 59, 99)( 60, 98)( 61, 97)( 62, 96);
poly := sub<Sym(124)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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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