Polytope of Type {6,52}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,52}*624a
Also Known As : {6,52|2}. if this polytope has another name.
Group : SmallGroup(624,179)
Rank : 3
Schlafli Type : {6,52}
Number of vertices, edges, etc : 6, 156, 52
Order of s₀s₁s₂ : 156
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,52,2} of size 1248
Vertex Figure Of :
   {2,6,52} of size 1248
   {3,6,52} of size 1872
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,26}*312
   3-fold quotients : {2,52}*208
   6-fold quotients : {2,26}*104
   12-fold quotients : {2,13}*52
   13-fold quotients : {6,4}*48a
   26-fold quotients : {6,2}*24
   39-fold quotients : {2,4}*16
   52-fold quotients : {3,2}*12
   78-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,104}*1248, {12,52}*1248
   3-fold covers : {18,52}*1872a, {6,156}*1872a, {6,156}*1872b
Permutation Representation (GAP) :

s0 := ( 14, 27)( 15, 28)( 16, 29)( 17, 30)( 18, 31)( 19, 32)( 20, 33)( 21, 34)
( 22, 35)( 23, 36)( 24, 37)( 25, 38)( 26, 39)( 53, 66)( 54, 67)( 55, 68)
( 56, 69)( 57, 70)( 58, 71)( 59, 72)( 60, 73)( 61, 74)( 62, 75)( 63, 76)
( 64, 77)( 65, 78)( 92,105)( 93,106)( 94,107)( 95,108)( 96,109)( 97,110)
( 98,111)( 99,112)(100,113)(101,114)(102,115)(103,116)(104,117)(131,144)
(132,145)(133,146)(134,147)(135,148)(136,149)(137,150)(138,151)(139,152)
(140,153)(141,154)(142,155)(143,156);;
s1 := (  1, 14)(  2, 26)(  3, 25)(  4, 24)(  5, 23)(  6, 22)(  7, 21)(  8, 20)
(  9, 19)( 10, 18)( 11, 17)( 12, 16)( 13, 15)( 28, 39)( 29, 38)( 30, 37)
( 31, 36)( 32, 35)( 33, 34)( 40, 53)( 41, 65)( 42, 64)( 43, 63)( 44, 62)
( 45, 61)( 46, 60)( 47, 59)( 48, 58)( 49, 57)( 50, 56)( 51, 55)( 52, 54)
( 67, 78)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79,131)( 80,143)
( 81,142)( 82,141)( 83,140)( 84,139)( 85,138)( 86,137)( 87,136)( 88,135)
( 89,134)( 90,133)( 91,132)( 92,118)( 93,130)( 94,129)( 95,128)( 96,127)
( 97,126)( 98,125)( 99,124)(100,123)(101,122)(102,121)(103,120)(104,119)
(105,144)(106,156)(107,155)(108,154)(109,153)(110,152)(111,151)(112,150)
(113,149)(114,148)(115,147)(116,146)(117,145);;
s2 := (  1, 80)(  2, 79)(  3, 91)(  4, 90)(  5, 89)(  6, 88)(  7, 87)(  8, 86)
(  9, 85)( 10, 84)( 11, 83)( 12, 82)( 13, 81)( 14, 93)( 15, 92)( 16,104)
( 17,103)( 18,102)( 19,101)( 20,100)( 21, 99)( 22, 98)( 23, 97)( 24, 96)
( 25, 95)( 26, 94)( 27,106)( 28,105)( 29,117)( 30,116)( 31,115)( 32,114)
( 33,113)( 34,112)( 35,111)( 36,110)( 37,109)( 38,108)( 39,107)( 40,119)
( 41,118)( 42,130)( 43,129)( 44,128)( 45,127)( 46,126)( 47,125)( 48,124)
( 49,123)( 50,122)( 51,121)( 52,120)( 53,132)( 54,131)( 55,143)( 56,142)
( 57,141)( 58,140)( 59,139)( 60,138)( 61,137)( 62,136)( 63,135)( 64,134)
( 65,133)( 66,145)( 67,144)( 68,156)( 69,155)( 70,154)( 71,153)( 72,152)
( 73,151)( 74,150)( 75,149)( 76,148)( 77,147)( 78,146);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(156)!( 14, 27)( 15, 28)( 16, 29)( 17, 30)( 18, 31)( 19, 32)( 20, 33)
( 21, 34)( 22, 35)( 23, 36)( 24, 37)( 25, 38)( 26, 39)( 53, 66)( 54, 67)
( 55, 68)( 56, 69)( 57, 70)( 58, 71)( 59, 72)( 60, 73)( 61, 74)( 62, 75)
( 63, 76)( 64, 77)( 65, 78)( 92,105)( 93,106)( 94,107)( 95,108)( 96,109)
( 97,110)( 98,111)( 99,112)(100,113)(101,114)(102,115)(103,116)(104,117)
(131,144)(132,145)(133,146)(134,147)(135,148)(136,149)(137,150)(138,151)
(139,152)(140,153)(141,154)(142,155)(143,156);
s1 := Sym(156)!(  1, 14)(  2, 26)(  3, 25)(  4, 24)(  5, 23)(  6, 22)(  7, 21)
(  8, 20)(  9, 19)( 10, 18)( 11, 17)( 12, 16)( 13, 15)( 28, 39)( 29, 38)
( 30, 37)( 31, 36)( 32, 35)( 33, 34)( 40, 53)( 41, 65)( 42, 64)( 43, 63)
( 44, 62)( 45, 61)( 46, 60)( 47, 59)( 48, 58)( 49, 57)( 50, 56)( 51, 55)
( 52, 54)( 67, 78)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79,131)
( 80,143)( 81,142)( 82,141)( 83,140)( 84,139)( 85,138)( 86,137)( 87,136)
( 88,135)( 89,134)( 90,133)( 91,132)( 92,118)( 93,130)( 94,129)( 95,128)
( 96,127)( 97,126)( 98,125)( 99,124)(100,123)(101,122)(102,121)(103,120)
(104,119)(105,144)(106,156)(107,155)(108,154)(109,153)(110,152)(111,151)
(112,150)(113,149)(114,148)(115,147)(116,146)(117,145);
s2 := Sym(156)!(  1, 80)(  2, 79)(  3, 91)(  4, 90)(  5, 89)(  6, 88)(  7, 87)
(  8, 86)(  9, 85)( 10, 84)( 11, 83)( 12, 82)( 13, 81)( 14, 93)( 15, 92)
( 16,104)( 17,103)( 18,102)( 19,101)( 20,100)( 21, 99)( 22, 98)( 23, 97)
( 24, 96)( 25, 95)( 26, 94)( 27,106)( 28,105)( 29,117)( 30,116)( 31,115)
( 32,114)( 33,113)( 34,112)( 35,111)( 36,110)( 37,109)( 38,108)( 39,107)
( 40,119)( 41,118)( 42,130)( 43,129)( 44,128)( 45,127)( 46,126)( 47,125)
( 48,124)( 49,123)( 50,122)( 51,121)( 52,120)( 53,132)( 54,131)( 55,143)
( 56,142)( 57,141)( 58,140)( 59,139)( 60,138)( 61,137)( 62,136)( 63,135)
( 64,134)( 65,133)( 66,145)( 67,144)( 68,156)( 69,155)( 70,154)( 71,153)
( 72,152)( 73,151)( 74,150)( 75,149)( 76,148)( 77,147)( 78,146);
poly := sub<Sym(156)|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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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 >;

References : None.
to this polytope