Polytope of Type {6,4,26}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4,26}*1248
Also Known As : {{6,4|2},{4,26|2}}. if this polytope has another name.
Group : SmallGroup(1248,1329)
Rank : 4
Schlafli Type : {6,4,26}
Number of vertices, edges, etc : 6, 12, 52, 26
Order of s₀s₁s₂s₃ : 156
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   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 : {6,2,26}*624
   3-fold quotients : {2,4,26}*416
   4-fold quotients : {3,2,26}*312, {6,2,13}*312
   6-fold quotients : {2,2,26}*208
   8-fold quotients : {3,2,13}*156
   12-fold quotients : {2,2,13}*104
   13-fold quotients : {6,4,2}*96a
   26-fold quotients : {6,2,2}*48
   39-fold quotients : {2,4,2}*32
   52-fold quotients : {3,2,2}*24
   78-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

References : None.
to this polytope