Polytope of Type {26,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {26,12}*624
Also Known As : {26,12|2}. if this polytope has another name.
Group : SmallGroup(624,178)
Rank : 3
Schlafli Type : {26,12}
Number of vertices, edges, etc : 26, 156, 12
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 :
   {26,12,2} of size 1248
Vertex Figure Of :
   {2,26,12} of size 1248
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {26,6}*312
   3-fold quotients : {26,4}*208
   6-fold quotients : {26,2}*104
   12-fold quotients : {13,2}*52
   13-fold quotients : {2,12}*48
   26-fold quotients : {2,6}*24
   39-fold quotients : {2,4}*16
   52-fold quotients : {2,3}*12
   78-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {26,24}*1248, {52,12}*1248
   3-fold covers : {26,36}*1872, {78,12}*1872a, {78,12}*1872b
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)( 80, 91)( 81, 90)( 82, 89)( 83, 88)
( 84, 87)( 85, 86)( 93,104)( 94,103)( 95,102)( 96,101)( 97,100)( 98, 99)
(106,117)(107,116)(108,115)(109,114)(110,113)(111,112)(119,130)(120,129)
(121,128)(122,127)(123,126)(124,125)(132,143)(133,142)(134,141)(135,140)
(136,139)(137,138)(145,156)(146,155)(147,154)(148,153)(149,152)(150,151);;
s1 := (  1,  2)(  3, 13)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 14, 28)( 15, 27)
( 16, 39)( 17, 38)( 18, 37)( 19, 36)( 20, 35)( 21, 34)( 22, 33)( 23, 32)
( 24, 31)( 25, 30)( 26, 29)( 40, 41)( 42, 52)( 43, 51)( 44, 50)( 45, 49)
( 46, 48)( 53, 67)( 54, 66)( 55, 78)( 56, 77)( 57, 76)( 58, 75)( 59, 74)
( 60, 73)( 61, 72)( 62, 71)( 63, 70)( 64, 69)( 65, 68)( 79,119)( 80,118)
( 81,130)( 82,129)( 83,128)( 84,127)( 85,126)( 86,125)( 87,124)( 88,123)
( 89,122)( 90,121)( 91,120)( 92,145)( 93,144)( 94,156)( 95,155)( 96,154)
( 97,153)( 98,152)( 99,151)(100,150)(101,149)(102,148)(103,147)(104,146)
(105,132)(106,131)(107,143)(108,142)(109,141)(110,140)(111,139)(112,138)
(113,137)(114,136)(115,135)(116,134)(117,133);;
s2 := (  1, 92)(  2, 93)(  3, 94)(  4, 95)(  5, 96)(  6, 97)(  7, 98)(  8, 99)
(  9,100)( 10,101)( 11,102)( 12,103)( 13,104)( 14, 79)( 15, 80)( 16, 81)
( 17, 82)( 18, 83)( 19, 84)( 20, 85)( 21, 86)( 22, 87)( 23, 88)( 24, 89)
( 25, 90)( 26, 91)( 27,105)( 28,106)( 29,107)( 30,108)( 31,109)( 32,110)
( 33,111)( 34,112)( 35,113)( 36,114)( 37,115)( 38,116)( 39,117)( 40,131)
( 41,132)( 42,133)( 43,134)( 44,135)( 45,136)( 46,137)( 47,138)( 48,139)
( 49,140)( 50,141)( 51,142)( 52,143)( 53,118)( 54,119)( 55,120)( 56,121)
( 57,122)( 58,123)( 59,124)( 60,125)( 61,126)( 62,127)( 63,128)( 64,129)
( 65,130)( 66,144)( 67,145)( 68,146)( 69,147)( 70,148)( 71,149)( 72,150)
( 73,151)( 74,152)( 75,153)( 76,154)( 77,155)( 78,156);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope