Polytope of Type {4,62}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,62}*496
Also Known As : {4,62|2}. if this polytope has another name.
Group : SmallGroup(496,31)
Rank : 3
Schlafli Type : {4,62}
Number of vertices, edges, etc : 4, 124, 62
Order of s₀s₁s₂ : 124
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,62,2} of size 992
   {4,62,4} of size 1984
Vertex Figure Of :
   {2,4,62} of size 992
   {4,4,62} of size 1984
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,62}*248
   4-fold quotients : {2,31}*124
   31-fold quotients : {4,2}*16
   62-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,124}*992, {8,62}*992
   3-fold covers : {12,62}*1488, {4,186}*1488a
   4-fold covers : {8,124}*1984a, {4,248}*1984a, {8,124}*1984b, {4,248}*1984b, {4,124}*1984, {16,62}*1984
Irregular Quotients (of which this is a minimal cover):
   None.

Permutation Representation (GAP) :

s0 := ( 63, 94)( 64, 95)( 65, 96)( 66, 97)( 67, 98)( 68, 99)( 69,100)( 70,101)( 71,102)( 72,103)( 73,104)( 74,105)( 75,106)( 76,107)( 77,108)( 78,109)( 79,110)( 80,111)( 81,112)( 82,113)( 83,114)( 84,115)( 85,116)( 86,117)( 87,118)( 88,119)( 89,120)( 90,121)( 91,122)( 92,123)( 93,124);;
s1 := (  1, 63)(  2, 93)(  3, 92)(  4, 91)(  5, 90)(  6, 89)(  7, 88)(  8, 87)(  9, 86)( 10, 85)( 11, 84)( 12, 83)( 13, 82)( 14, 81)( 15, 80)( 16, 79)( 17, 78)( 18, 77)( 19, 76)( 20, 75)( 21, 74)( 22, 73)( 23, 72)( 24, 71)( 25, 70)( 26, 69)( 27, 68)( 28, 67)( 29, 66)( 30, 65)( 31, 64)( 32, 94)( 33,124)( 34,123)( 35,122)( 36,121)( 37,120)( 38,119)( 39,118)( 40,117)( 41,116)( 42,115)( 43,114)( 44,113)( 45,112)( 46,111)( 47,110)( 48,109)( 49,108)( 50,107)( 51,106)( 52,105)( 53,104)( 54,103)( 55,102)( 56,101)( 57,100)( 58, 99)( 59, 98)( 60, 97)( 61, 96)( 62, 95);;
s2 := (  1,  2)(  3, 31)(  4, 30)(  5, 29)(  6, 28)(  7, 27)(  8, 26)(  9, 25)( 10, 24)( 11, 23)( 12, 22)( 13, 21)( 14, 20)( 15, 19)( 16, 18)( 32, 33)( 34, 62)( 35, 61)( 36, 60)( 37, 59)( 38, 58)( 39, 57)( 40, 56)( 41, 55)( 42, 54)( 43, 53)( 44, 52)( 45, 51)( 46, 50)( 47, 49)( 63, 64)( 65, 93)( 66, 92)( 67, 91)( 68, 90)( 69, 89)( 70, 88)( 71, 87)( 72, 86)( 73, 85)( 74, 84)( 75, 83)( 76, 82)( 77, 81)( 78, 80)( 94, 95)( 96,124)( 97,123)( 98,122)( 99,121)(100,120)(101,119)(102,118)(103,117)(104,116)(105,115)(106,114)(107,113)(108,112)(109,111);;
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(124)!( 63, 94)( 64, 95)( 65, 96)( 66, 97)( 67, 98)( 68, 99)( 69,100)( 70,101)( 71,102)( 72,103)( 73,104)( 74,105)( 75,106)( 76,107)( 77,108)( 78,109)( 79,110)( 80,111)( 81,112)( 82,113)( 83,114)( 84,115)( 85,116)( 86,117)( 87,118)( 88,119)( 89,120)( 90,121)( 91,122)( 92,123)( 93,124);
s1 := Sym(124)!(  1, 63)(  2, 93)(  3, 92)(  4, 91)(  5, 90)(  6, 89)(  7, 88)(  8, 87)(  9, 86)( 10, 85)( 11, 84)( 12, 83)( 13, 82)( 14, 81)( 15, 80)( 16, 79)( 17, 78)( 18, 77)( 19, 76)( 20, 75)( 21, 74)( 22, 73)( 23, 72)( 24, 71)( 25, 70)( 26, 69)( 27, 68)( 28, 67)( 29, 66)( 30, 65)( 31, 64)( 32, 94)( 33,124)( 34,123)( 35,122)( 36,121)( 37,120)( 38,119)( 39,118)( 40,117)( 41,116)( 42,115)( 43,114)( 44,113)( 45,112)( 46,111)( 47,110)( 48,109)( 49,108)( 50,107)( 51,106)( 52,105)( 53,104)( 54,103)( 55,102)( 56,101)( 57,100)( 58, 99)( 59, 98)( 60, 97)( 61, 96)( 62, 95);
s2 := Sym(124)!(  1,  2)(  3, 31)(  4, 30)(  5, 29)(  6, 28)(  7, 27)(  8, 26)(  9, 25)( 10, 24)( 11, 23)( 12, 22)( 13, 21)( 14, 20)( 15, 19)( 16, 18)( 32, 33)( 34, 62)( 35, 61)( 36, 60)( 37, 59)( 38, 58)( 39, 57)( 40, 56)( 41, 55)( 42, 54)( 43, 53)( 44, 52)( 45, 51)( 46, 50)( 47, 49)( 63, 64)( 65, 93)( 66, 92)( 67, 91)( 68, 90)( 69, 89)( 70, 88)( 71, 87)( 72, 86)( 73, 85)( 74, 84)( 75, 83)( 76, 82)( 77, 81)( 78, 80)( 94, 95)( 96,124)( 97,123)( 98,122)( 99,121)(100,120)(101,119)(102,118)(103,117)(104,116)(105,115)(106,114)(107,113)(108,112)(109,111);
poly := sub<Sym(124)|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, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope

Polytope of Type {4,62}

Twisty Puzzle