Polytope of Type {26,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {26,6,4}*1248a
Also Known As : {{26,6|2},{6,4|2}}. if this polytope has another name.
Group : SmallGroup(1248,1329)
Rank : 4
Schlafli Type : {26,6,4}
Number of vertices, edges, etc : 26, 78, 12, 4
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 : {26,6,2}*624
   3-fold quotients : {26,2,4}*416
   6-fold quotients : {13,2,4}*208, {26,2,2}*208
   12-fold quotients : {13,2,2}*104
   13-fold quotients : {2,6,4}*96a
   26-fold quotients : {2,6,2}*48
   39-fold quotients : {2,2,4}*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 := (  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, 80)( 81, 91)
( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 92,106)( 93,105)( 94,117)( 95,116)
( 96,115)( 97,114)( 98,113)( 99,112)(100,111)(101,110)(102,109)(103,108)
(104,107)(118,119)(120,130)(121,129)(122,128)(123,127)(124,126)(131,145)
(132,144)(133,156)(134,155)(135,154)(136,153)(137,152)(138,151)(139,150)
(140,149)(141,148)(142,147)(143,146);;
s2 := (  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);;
s3 := (  1, 79)(  2, 80)(  3, 81)(  4, 82)(  5, 83)(  6, 84)(  7, 85)(  8, 86)
(  9, 87)( 10, 88)( 11, 89)( 12, 90)( 13, 91)( 14, 92)( 15, 93)( 16, 94)
( 17, 95)( 18, 96)( 19, 97)( 20, 98)( 21, 99)( 22,100)( 23,101)( 24,102)
( 25,103)( 26,104)( 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)( 40,118)
( 41,119)( 42,120)( 43,121)( 44,122)( 45,123)( 46,124)( 47,125)( 48,126)
( 49,127)( 50,128)( 51,129)( 52,130)( 53,131)( 54,132)( 55,133)( 56,134)
( 57,135)( 58,136)( 59,137)( 60,138)( 61,139)( 62,140)( 63,141)( 64,142)
( 65,143)( 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,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*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
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, 80)
( 81, 91)( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 92,106)( 93,105)( 94,117)
( 95,116)( 96,115)( 97,114)( 98,113)( 99,112)(100,111)(101,110)(102,109)
(103,108)(104,107)(118,119)(120,130)(121,129)(122,128)(123,127)(124,126)
(131,145)(132,144)(133,156)(134,155)(135,154)(136,153)(137,152)(138,151)
(139,150)(140,149)(141,148)(142,147)(143,146);
s2 := 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);
s3 := Sym(156)!(  1, 79)(  2, 80)(  3, 81)(  4, 82)(  5, 83)(  6, 84)(  7, 85)
(  8, 86)(  9, 87)( 10, 88)( 11, 89)( 12, 90)( 13, 91)( 14, 92)( 15, 93)
( 16, 94)( 17, 95)( 18, 96)( 19, 97)( 20, 98)( 21, 99)( 22,100)( 23,101)
( 24,102)( 25,103)( 26,104)( 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)
( 40,118)( 41,119)( 42,120)( 43,121)( 44,122)( 45,123)( 46,124)( 47,125)
( 48,126)( 49,127)( 50,128)( 51,129)( 52,130)( 53,131)( 54,132)( 55,133)
( 56,134)( 57,135)( 58,136)( 59,137)( 60,138)( 61,139)( 62,140)( 63,141)
( 64,142)( 65,143)( 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,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*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, 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