Polytope of Type {62,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {62,4}*496
Also Known As : {62,4|2}. if this polytope has another name.
Group : SmallGroup(496,31)
Rank : 3
Schlafli Type : {62,4}
Number of vertices, edges, etc : 62, 124, 4
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 :
   {62,4,2} of size 992
   {62,4,4} of size 1984
Vertex Figure Of :
   {2,62,4} of size 992
   {4,62,4} of size 1984
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {62,2}*248
   4-fold quotients : {31,2}*124
   31-fold quotients : {2,4}*16
   62-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {124,4}*992, {62,8}*992
   3-fold covers : {62,12}*1488, {186,4}*1488a
   4-fold covers : {124,8}*1984a, {248,4}*1984a, {124,8}*1984b, {248,4}*1984b, {124,4}*1984, {62,16}*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)( 64, 93)( 65, 92)
( 66, 91)( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71, 86)( 72, 85)( 73, 84)
( 74, 83)( 75, 82)( 76, 81)( 77, 80)( 78, 79)( 95,124)( 96,123)( 97,122)
( 98,121)( 99,120)(100,119)(101,118)(102,117)(103,116)(104,115)(105,114)
(106,113)(107,112)(108,111)(109,110);;
s1 := (  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, 95)( 64, 94)
( 65,124)( 66,123)( 67,122)( 68,121)( 69,120)( 70,119)( 71,118)( 72,117)
( 73,116)( 74,115)( 75,114)( 76,113)( 77,112)( 78,111)( 79,110)( 80,109)
( 81,108)( 82,107)( 83,106)( 84,105)( 85,104)( 86,103)( 87,102)( 88,101)
( 89,100)( 90, 99)( 91, 98)( 92, 97)( 93, 96);;
s2 := (  1, 63)(  2, 64)(  3, 65)(  4, 66)(  5, 67)(  6, 68)(  7, 69)(  8, 70)
(  9, 71)( 10, 72)( 11, 73)( 12, 74)( 13, 75)( 14, 76)( 15, 77)( 16, 78)
( 17, 79)( 18, 80)( 19, 81)( 20, 82)( 21, 83)( 22, 84)( 23, 85)( 24, 86)
( 25, 87)( 26, 88)( 27, 89)( 28, 90)( 29, 91)( 30, 92)( 31, 93)( 32, 94)
( 33, 95)( 34, 96)( 35, 97)( 36, 98)( 37, 99)( 38,100)( 39,101)( 40,102)
( 41,103)( 42,104)( 43,105)( 44,106)( 45,107)( 46,108)( 47,109)( 48,110)
( 49,111)( 50,112)( 51,113)( 52,114)( 53,115)( 54,116)( 55,117)( 56,118)
( 57,119)( 58,120)( 59,121)( 60,122)( 61,123)( 62,124);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*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 ];;
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)( 64, 93)
( 65, 92)( 66, 91)( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71, 86)( 72, 85)
( 73, 84)( 74, 83)( 75, 82)( 76, 81)( 77, 80)( 78, 79)( 95,124)( 96,123)
( 97,122)( 98,121)( 99,120)(100,119)(101,118)(102,117)(103,116)(104,115)
(105,114)(106,113)(107,112)(108,111)(109,110);
s1 := 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, 95)
( 64, 94)( 65,124)( 66,123)( 67,122)( 68,121)( 69,120)( 70,119)( 71,118)
( 72,117)( 73,116)( 74,115)( 75,114)( 76,113)( 77,112)( 78,111)( 79,110)
( 80,109)( 81,108)( 82,107)( 83,106)( 84,105)( 85,104)( 86,103)( 87,102)
( 88,101)( 89,100)( 90, 99)( 91, 98)( 92, 97)( 93, 96);
s2 := Sym(124)!(  1, 63)(  2, 64)(  3, 65)(  4, 66)(  5, 67)(  6, 68)(  7, 69)
(  8, 70)(  9, 71)( 10, 72)( 11, 73)( 12, 74)( 13, 75)( 14, 76)( 15, 77)
( 16, 78)( 17, 79)( 18, 80)( 19, 81)( 20, 82)( 21, 83)( 22, 84)( 23, 85)
( 24, 86)( 25, 87)( 26, 88)( 27, 89)( 28, 90)( 29, 91)( 30, 92)( 31, 93)
( 32, 94)( 33, 95)( 34, 96)( 35, 97)( 36, 98)( 37, 99)( 38,100)( 39,101)
( 40,102)( 41,103)( 42,104)( 43,105)( 44,106)( 45,107)( 46,108)( 47,109)
( 48,110)( 49,111)( 50,112)( 51,113)( 52,114)( 53,115)( 54,116)( 55,117)
( 56,118)( 57,119)( 58,120)( 59,121)( 60,122)( 61,123)( 62,124);
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*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 >;

References : None.
to this polytope