Polytope of Type {2,12,26}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,26}*1248
if this polytope has a name.
Group : SmallGroup(1248,1319)
Rank : 4
Schlafli Type : {2,12,26}
Number of vertices, edges, etc : 2, 12, 156, 26
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 : {2,6,26}*624
   3-fold quotients : {2,4,26}*416
   6-fold quotients : {2,2,26}*208
   12-fold quotients : {2,2,13}*104
   13-fold quotients : {2,12,2}*96
   26-fold quotients : {2,6,2}*48
   39-fold quotients : {2,4,2}*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 := (1,2);;
s1 := ( 16, 29)( 17, 30)( 18, 31)( 19, 32)( 20, 33)( 21, 34)( 22, 35)( 23, 36)
( 24, 37)( 25, 38)( 26, 39)( 27, 40)( 28, 41)( 55, 68)( 56, 69)( 57, 70)
( 58, 71)( 59, 72)( 60, 73)( 61, 74)( 62, 75)( 63, 76)( 64, 77)( 65, 78)
( 66, 79)( 67, 80)( 81,120)( 82,121)( 83,122)( 84,123)( 85,124)( 86,125)
( 87,126)( 88,127)( 89,128)( 90,129)( 91,130)( 92,131)( 93,132)( 94,146)
( 95,147)( 96,148)( 97,149)( 98,150)( 99,151)(100,152)(101,153)(102,154)
(103,155)(104,156)(105,157)(106,158)(107,133)(108,134)(109,135)(110,136)
(111,137)(112,138)(113,139)(114,140)(115,141)(116,142)(117,143)(118,144)
(119,145);;
s2 := (  3, 94)(  4,106)(  5,105)(  6,104)(  7,103)(  8,102)(  9,101)( 10,100)
( 11, 99)( 12, 98)( 13, 97)( 14, 96)( 15, 95)( 16, 81)( 17, 93)( 18, 92)
( 19, 91)( 20, 90)( 21, 89)( 22, 88)( 23, 87)( 24, 86)( 25, 85)( 26, 84)
( 27, 83)( 28, 82)( 29,107)( 30,119)( 31,118)( 32,117)( 33,116)( 34,115)
( 35,114)( 36,113)( 37,112)( 38,111)( 39,110)( 40,109)( 41,108)( 42,133)
( 43,145)( 44,144)( 45,143)( 46,142)( 47,141)( 48,140)( 49,139)( 50,138)
( 51,137)( 52,136)( 53,135)( 54,134)( 55,120)( 56,132)( 57,131)( 58,130)
( 59,129)( 60,128)( 61,127)( 62,126)( 63,125)( 64,124)( 65,123)( 66,122)
( 67,121)( 68,146)( 69,158)( 70,157)( 71,156)( 72,155)( 73,154)( 74,153)
( 75,152)( 76,151)( 77,150)( 78,149)( 79,148)( 80,147);;
s3 := (  3,  4)(  5, 15)(  6, 14)(  7, 13)(  8, 12)(  9, 11)( 16, 17)( 18, 28)
( 19, 27)( 20, 26)( 21, 25)( 22, 24)( 29, 30)( 31, 41)( 32, 40)( 33, 39)
( 34, 38)( 35, 37)( 42, 43)( 44, 54)( 45, 53)( 46, 52)( 47, 51)( 48, 50)
( 55, 56)( 57, 67)( 58, 66)( 59, 65)( 60, 64)( 61, 63)( 68, 69)( 70, 80)
( 71, 79)( 72, 78)( 73, 77)( 74, 76)( 81, 82)( 83, 93)( 84, 92)( 85, 91)
( 86, 90)( 87, 89)( 94, 95)( 96,106)( 97,105)( 98,104)( 99,103)(100,102)
(107,108)(109,119)(110,118)(111,117)(112,116)(113,115)(120,121)(122,132)
(123,131)(124,130)(125,129)(126,128)(133,134)(135,145)(136,144)(137,143)
(138,142)(139,141)(146,147)(148,158)(149,157)(150,156)(151,155)(152,154);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(158)!(1,2);
s1 := Sym(158)!( 16, 29)( 17, 30)( 18, 31)( 19, 32)( 20, 33)( 21, 34)( 22, 35)
( 23, 36)( 24, 37)( 25, 38)( 26, 39)( 27, 40)( 28, 41)( 55, 68)( 56, 69)
( 57, 70)( 58, 71)( 59, 72)( 60, 73)( 61, 74)( 62, 75)( 63, 76)( 64, 77)
( 65, 78)( 66, 79)( 67, 80)( 81,120)( 82,121)( 83,122)( 84,123)( 85,124)
( 86,125)( 87,126)( 88,127)( 89,128)( 90,129)( 91,130)( 92,131)( 93,132)
( 94,146)( 95,147)( 96,148)( 97,149)( 98,150)( 99,151)(100,152)(101,153)
(102,154)(103,155)(104,156)(105,157)(106,158)(107,133)(108,134)(109,135)
(110,136)(111,137)(112,138)(113,139)(114,140)(115,141)(116,142)(117,143)
(118,144)(119,145);
s2 := Sym(158)!(  3, 94)(  4,106)(  5,105)(  6,104)(  7,103)(  8,102)(  9,101)
( 10,100)( 11, 99)( 12, 98)( 13, 97)( 14, 96)( 15, 95)( 16, 81)( 17, 93)
( 18, 92)( 19, 91)( 20, 90)( 21, 89)( 22, 88)( 23, 87)( 24, 86)( 25, 85)
( 26, 84)( 27, 83)( 28, 82)( 29,107)( 30,119)( 31,118)( 32,117)( 33,116)
( 34,115)( 35,114)( 36,113)( 37,112)( 38,111)( 39,110)( 40,109)( 41,108)
( 42,133)( 43,145)( 44,144)( 45,143)( 46,142)( 47,141)( 48,140)( 49,139)
( 50,138)( 51,137)( 52,136)( 53,135)( 54,134)( 55,120)( 56,132)( 57,131)
( 58,130)( 59,129)( 60,128)( 61,127)( 62,126)( 63,125)( 64,124)( 65,123)
( 66,122)( 67,121)( 68,146)( 69,158)( 70,157)( 71,156)( 72,155)( 73,154)
( 74,153)( 75,152)( 76,151)( 77,150)( 78,149)( 79,148)( 80,147);
s3 := Sym(158)!(  3,  4)(  5, 15)(  6, 14)(  7, 13)(  8, 12)(  9, 11)( 16, 17)
( 18, 28)( 19, 27)( 20, 26)( 21, 25)( 22, 24)( 29, 30)( 31, 41)( 32, 40)
( 33, 39)( 34, 38)( 35, 37)( 42, 43)( 44, 54)( 45, 53)( 46, 52)( 47, 51)
( 48, 50)( 55, 56)( 57, 67)( 58, 66)( 59, 65)( 60, 64)( 61, 63)( 68, 69)
( 70, 80)( 71, 79)( 72, 78)( 73, 77)( 74, 76)( 81, 82)( 83, 93)( 84, 92)
( 85, 91)( 86, 90)( 87, 89)( 94, 95)( 96,106)( 97,105)( 98,104)( 99,103)
(100,102)(107,108)(109,119)(110,118)(111,117)(112,116)(113,115)(120,121)
(122,132)(123,131)(124,130)(125,129)(126,128)(133,134)(135,145)(136,144)
(137,143)(138,142)(139,141)(146,147)(148,158)(149,157)(150,156)(151,155)
(152,154);
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope