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