Polytope of Type {2,26,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,26,12}*1248
if this polytope has a name.
Group : SmallGroup(1248,1319)
Rank : 4
Schlafli Type : {2,26,12}
Number of vertices, edges, etc : 2, 26, 156, 12
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 : {2,26,6}*624
3-fold quotients : {2,26,4}*416
6-fold quotients : {2,26,2}*208
12-fold quotients : {2,13,2}*104
13-fold quotients : {2,2,12}*96
26-fold quotients : {2,2,6}*48
39-fold quotients : {2,2,4}*32
52-fold quotients : {2,2,3}*24
78-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 15)( 5, 14)( 6, 13)( 7, 12)( 8, 11)( 9, 10)( 17, 28)( 18, 27)( 19, 26)( 20, 25)( 21, 24)( 22, 23)( 30, 41)( 31, 40)( 32, 39)( 33, 38)( 34, 37)( 35, 36)( 43, 54)( 44, 53)( 45, 52)( 46, 51)( 47, 50)( 48, 49)( 56, 67)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 69, 80)( 70, 79)( 71, 78)( 72, 77)( 73, 76)( 74, 75)( 82, 93)( 83, 92)( 84, 91)( 85, 90)( 86, 89)( 87, 88)( 95,106)( 96,105)( 97,104)( 98,103)( 99,102)(100,101)(108,119)(109,118)(110,117)(111,116)(112,115)(113,114)(121,132)(122,131)(123,130)(124,129)(125,128)(126,127)(134,145)(135,144)(136,143)(137,142)(138,141)(139,140)(147,158)(148,157)(149,156)(150,155)(151,154)(152,153);;
s2 := ( 3, 4)( 5, 15)( 6, 14)( 7, 13)( 8, 12)( 9, 11)( 16, 30)( 17, 29)( 18, 41)( 19, 40)( 20, 39)( 21, 38)( 22, 37)( 23, 36)( 24, 35)( 25, 34)( 26, 33)( 27, 32)( 28, 31)( 42, 43)( 44, 54)( 45, 53)( 46, 52)( 47, 51)( 48, 50)( 55, 69)( 56, 68)( 57, 80)( 58, 79)( 59, 78)( 60, 77)( 61, 76)( 62, 75)( 63, 74)( 64, 73)( 65, 72)( 66, 71)( 67, 70)( 81,121)( 82,120)( 83,132)( 84,131)( 85,130)( 86,129)( 87,128)( 88,127)( 89,126)( 90,125)( 91,124)( 92,123)( 93,122)( 94,147)( 95,146)( 96,158)( 97,157)( 98,156)( 99,155)(100,154)(101,153)(102,152)(103,151)(104,150)(105,149)(106,148)(107,134)(108,133)(109,145)(110,144)(111,143)(112,142)(113,141)(114,140)(115,139)(116,138)(117,137)(118,136)(119,135);;
s3 := ( 3, 94)( 4, 95)( 5, 96)( 6, 97)( 7, 98)( 8, 99)( 9,100)( 10,101)( 11,102)( 12,103)( 13,104)( 14,105)( 15,106)( 16, 81)( 17, 82)( 18, 83)( 19, 84)( 20, 85)( 21, 86)( 22, 87)( 23, 88)( 24, 89)( 25, 90)( 26, 91)( 27, 92)( 28, 93)( 29,107)( 30,108)( 31,109)( 32,110)( 33,111)( 34,112)( 35,113)( 36,114)( 37,115)( 38,116)( 39,117)( 40,118)( 41,119)( 42,133)( 43,134)( 44,135)( 45,136)( 46,137)( 47,138)( 48,139)( 49,140)( 50,141)( 51,142)( 52,143)( 53,144)( 54,145)( 55,120)( 56,121)( 57,122)( 58,123)( 59,124)( 60,125)( 61,126)( 62,127)( 63,128)( 64,129)( 65,130)( 66,131)( 67,132)( 68,146)( 69,147)( 70,148)( 71,149)( 72,150)( 73,151)( 74,152)( 75,153)( 76,154)( 77,155)( 78,156)( 79,157)( 80,158);;
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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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(158)!(1,2);
s1 := Sym(158)!( 4, 15)( 5, 14)( 6, 13)( 7, 12)( 8, 11)( 9, 10)( 17, 28)( 18, 27)( 19, 26)( 20, 25)( 21, 24)( 22, 23)( 30, 41)( 31, 40)( 32, 39)( 33, 38)( 34, 37)( 35, 36)( 43, 54)( 44, 53)( 45, 52)( 46, 51)( 47, 50)( 48, 49)( 56, 67)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 69, 80)( 70, 79)( 71, 78)( 72, 77)( 73, 76)( 74, 75)( 82, 93)( 83, 92)( 84, 91)( 85, 90)( 86, 89)( 87, 88)( 95,106)( 96,105)( 97,104)( 98,103)( 99,102)(100,101)(108,119)(109,118)(110,117)(111,116)(112,115)(113,114)(121,132)(122,131)(123,130)(124,129)(125,128)(126,127)(134,145)(135,144)(136,143)(137,142)(138,141)(139,140)(147,158)(148,157)(149,156)(150,155)(151,154)(152,153);
s2 := Sym(158)!( 3, 4)( 5, 15)( 6, 14)( 7, 13)( 8, 12)( 9, 11)( 16, 30)( 17, 29)( 18, 41)( 19, 40)( 20, 39)( 21, 38)( 22, 37)( 23, 36)( 24, 35)( 25, 34)( 26, 33)( 27, 32)( 28, 31)( 42, 43)( 44, 54)( 45, 53)( 46, 52)( 47, 51)( 48, 50)( 55, 69)( 56, 68)( 57, 80)( 58, 79)( 59, 78)( 60, 77)( 61, 76)( 62, 75)( 63, 74)( 64, 73)( 65, 72)( 66, 71)( 67, 70)( 81,121)( 82,120)( 83,132)( 84,131)( 85,130)( 86,129)( 87,128)( 88,127)( 89,126)( 90,125)( 91,124)( 92,123)( 93,122)( 94,147)( 95,146)( 96,158)( 97,157)( 98,156)( 99,155)(100,154)(101,153)(102,152)(103,151)(104,150)(105,149)(106,148)(107,134)(108,133)(109,145)(110,144)(111,143)(112,142)(113,141)(114,140)(115,139)(116,138)(117,137)(118,136)(119,135);
s3 := Sym(158)!( 3, 94)( 4, 95)( 5, 96)( 6, 97)( 7, 98)( 8, 99)( 9,100)( 10,101)( 11,102)( 12,103)( 13,104)( 14,105)( 15,106)( 16, 81)( 17, 82)( 18, 83)( 19, 84)( 20, 85)( 21, 86)( 22, 87)( 23, 88)( 24, 89)( 25, 90)( 26, 91)( 27, 92)( 28, 93)( 29,107)( 30,108)( 31,109)( 32,110)( 33,111)( 34,112)( 35,113)( 36,114)( 37,115)( 38,116)( 39,117)( 40,118)( 41,119)( 42,133)( 43,134)( 44,135)( 45,136)( 46,137)( 47,138)( 48,139)( 49,140)( 50,141)( 51,142)( 52,143)( 53,144)( 54,145)( 55,120)( 56,121)( 57,122)( 58,123)( 59,124)( 60,125)( 61,126)( 62,127)( 63,128)( 64,129)( 65,130)( 66,131)( 67,132)( 68,146)( 69,147)( 70,148)( 71,149)( 72,150)( 73,151)( 74,152)( 75,153)( 76,154)( 77,155)( 78,156)( 79,157)( 80,158);
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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 >;
to this polytope