Polytope of Type {52,6,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {52,6,2}*1248a
if this polytope has a name.
Group : SmallGroup(1248,1320)
Rank : 4
Schlafli Type : {52,6,2}
Number of vertices, edges, etc : 52, 156, 6, 2
Order of s0s1s2s3 : 156
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {26,6,2}*624
3-fold quotients : {52,2,2}*416
6-fold quotients : {26,2,2}*208
12-fold quotients : {13,2,2}*104
13-fold quotients : {4,6,2}*96a
26-fold quotients : {2,6,2}*48
39-fold quotients : {4,2,2}*32
52-fold quotients : {2,3,2}*24
78-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 13)( 3, 12)( 4, 11)( 5, 10)( 6, 9)( 7, 8)( 15, 26)( 16, 25)( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 28, 39)( 29, 38)( 30, 37)( 31, 36)( 32, 35)( 33, 34)( 41, 52)( 42, 51)( 43, 50)( 44, 49)( 45, 48)( 46, 47)( 54, 65)( 55, 64)( 56, 63)( 57, 62)( 58, 61)( 59, 60)( 67, 78)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79,118)( 80,130)( 81,129)( 82,128)( 83,127)( 84,126)( 85,125)( 86,124)( 87,123)( 88,122)( 89,121)( 90,120)( 91,119)( 92,131)( 93,143)( 94,142)( 95,141)( 96,140)( 97,139)( 98,138)( 99,137)(100,136)(101,135)(102,134)(103,133)(104,132)(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);;
s1 := ( 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)( 14,106)( 15,105)( 16,117)( 17,116)( 18,115)( 19,114)( 20,113)( 21,112)( 22,111)( 23,110)( 24,109)( 25,108)( 26,107)( 27, 93)( 28, 92)( 29,104)( 30,103)( 31,102)( 32,101)( 33,100)( 34, 99)( 35, 98)( 36, 97)( 37, 96)( 38, 95)( 39, 94)( 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)( 53,145)( 54,144)( 55,156)( 56,155)( 57,154)( 58,153)( 59,152)( 60,151)( 61,150)( 62,149)( 63,148)( 64,147)( 65,146)( 66,132)( 67,131)( 68,143)( 69,142)( 70,141)( 71,140)( 72,139)( 73,138)( 74,137)( 75,136)( 76,135)( 77,134)( 78,133);;
s2 := ( 1, 14)( 2, 15)( 3, 16)( 4, 17)( 5, 18)( 6, 19)( 7, 20)( 8, 21)( 9, 22)( 10, 23)( 11, 24)( 12, 25)( 13, 26)( 40, 53)( 41, 54)( 42, 55)( 43, 56)( 44, 57)( 45, 58)( 46, 59)( 47, 60)( 48, 61)( 49, 62)( 50, 63)( 51, 64)( 52, 65)( 79, 92)( 80, 93)( 81, 94)( 82, 95)( 83, 96)( 84, 97)( 85, 98)( 86, 99)( 87,100)( 88,101)( 89,102)( 90,103)( 91,104)(118,131)(119,132)(120,133)(121,134)(122,135)(123,136)(124,137)(125,138)(126,139)(127,140)(128,141)(129,142)(130,143);;
s3 := (157,158);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(158)!( 2, 13)( 3, 12)( 4, 11)( 5, 10)( 6, 9)( 7, 8)( 15, 26)( 16, 25)( 17, 24)( 18, 23)( 19, 22)( 20, 21)( 28, 39)( 29, 38)( 30, 37)( 31, 36)( 32, 35)( 33, 34)( 41, 52)( 42, 51)( 43, 50)( 44, 49)( 45, 48)( 46, 47)( 54, 65)( 55, 64)( 56, 63)( 57, 62)( 58, 61)( 59, 60)( 67, 78)( 68, 77)( 69, 76)( 70, 75)( 71, 74)( 72, 73)( 79,118)( 80,130)( 81,129)( 82,128)( 83,127)( 84,126)( 85,125)( 86,124)( 87,123)( 88,122)( 89,121)( 90,120)( 91,119)( 92,131)( 93,143)( 94,142)( 95,141)( 96,140)( 97,139)( 98,138)( 99,137)(100,136)(101,135)(102,134)(103,133)(104,132)(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);
s1 := Sym(158)!( 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)( 14,106)( 15,105)( 16,117)( 17,116)( 18,115)( 19,114)( 20,113)( 21,112)( 22,111)( 23,110)( 24,109)( 25,108)( 26,107)( 27, 93)( 28, 92)( 29,104)( 30,103)( 31,102)( 32,101)( 33,100)( 34, 99)( 35, 98)( 36, 97)( 37, 96)( 38, 95)( 39, 94)( 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)( 53,145)( 54,144)( 55,156)( 56,155)( 57,154)( 58,153)( 59,152)( 60,151)( 61,150)( 62,149)( 63,148)( 64,147)( 65,146)( 66,132)( 67,131)( 68,143)( 69,142)( 70,141)( 71,140)( 72,139)( 73,138)( 74,137)( 75,136)( 76,135)( 77,134)( 78,133);
s2 := Sym(158)!( 1, 14)( 2, 15)( 3, 16)( 4, 17)( 5, 18)( 6, 19)( 7, 20)( 8, 21)( 9, 22)( 10, 23)( 11, 24)( 12, 25)( 13, 26)( 40, 53)( 41, 54)( 42, 55)( 43, 56)( 44, 57)( 45, 58)( 46, 59)( 47, 60)( 48, 61)( 49, 62)( 50, 63)( 51, 64)( 52, 65)( 79, 92)( 80, 93)( 81, 94)( 82, 95)( 83, 96)( 84, 97)( 85, 98)( 86, 99)( 87,100)( 88,101)( 89,102)( 90,103)( 91,104)(118,131)(119,132)(120,133)(121,134)(122,135)(123,136)(124,137)(125,138)(126,139)(127,140)(128,141)(129,142)(130,143);
s3 := Sym(158)!(157,158);
poly := sub<Sym(158)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*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 >;
to this polytope