Overview
- Group
- SmallGroup(1248,1329)
- Rank
- 4
- Schläfli Type
- {4,26,6}
- Vertices, edges, …
- 4, 52, 78, 6
- Order of s0s1s2s3
- 156
- Order of s0s1s2s3s2s1
- 2
- Also known as
- {{4,26|2},{26,6|2}}. if this polytope has another name.
Special Properties
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
6-fold
12-fold
13-fold
26-fold
39-fold
52-fold
78-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 79,118)( 80,119)( 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)( 94,133)( 95,134)( 96,135)( 97,136)( 98,137)( 99,138)(100,139)(101,140)(102,141)(103,142)(104,143)(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);; s1 := ( 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);; s2 := ( 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);; s3 := ( 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, 92)( 80, 93)( 81, 94)( 82, 95)( 83, 96)( 84, 97)( 85, 98)( 86, 99)( 87,100)( 88,101)( 89,102)( 90,103)( 91,104)(118,131)(119,132)(120,133)(121,134)(122,135)(123,136)(124,137)(125,138)(126,139)(127,140)(128,141)(129,142)(130,143);; 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*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2,
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(156)!( 79,118)( 80,119)( 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)( 94,133)( 95,134)( 96,135)( 97,136)( 98,137)( 99,138)(100,139)(101,140)(102,141)(103,142)(104,143)(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); s1 := 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); s2 := 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); s3 := 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, 92)( 80, 93)( 81, 94)( 82, 95)( 83, 96)( 84, 97)( 85, 98)( 86, 99)( 87,100)( 88,101)( 89,102)( 90,103)( 91,104)(118,131)(119,132)(120,133)(121,134)(122,135)(123,136)(124,137)(125,138)(126,139)(127,140)(128,141)(129,142)(130,143); 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*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 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 >;
References
None.
to this polytope.