Overview
- Group
- SmallGroup(1344,11133)
- Rank
- 4
- Schläfli Type
- {8,42,2}
- Vertices, edges, …
- 8, 168, 42, 2
- Order of s0s1s2s3
- 168
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
7-fold
8-fold
12-fold
14-fold
21-fold
24-fold
28-fold
42-fold
56-fold
84-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 43, 64)( 44, 65)( 45, 66)( 46, 67)( 47, 68)( 48, 69)( 49, 70)( 50, 71)( 51, 72)( 52, 73)( 53, 74)( 54, 75)( 55, 76)( 56, 77)( 57, 78)( 58, 79)( 59, 80)( 60, 81)( 61, 82)( 62, 83)( 63, 84)( 85,127)( 86,128)( 87,129)( 88,130)( 89,131)( 90,132)( 91,133)( 92,134)( 93,135)( 94,136)( 95,137)( 96,138)( 97,139)( 98,140)( 99,141)(100,142)(101,143)(102,144)(103,145)(104,146)(105,147)(106,148)(107,149)(108,150)(109,151)(110,152)(111,153)(112,154)(113,155)(114,156)(115,157)(116,158)(117,159)(118,160)(119,161)(120,162)(121,163)(122,164)(123,165)(124,166)(125,167)(126,168);; s1 := ( 1, 85)( 2, 91)( 3, 90)( 4, 89)( 5, 88)( 6, 87)( 7, 86)( 8, 99)( 9,105)( 10,104)( 11,103)( 12,102)( 13,101)( 14,100)( 15, 92)( 16, 98)( 17, 97)( 18, 96)( 19, 95)( 20, 94)( 21, 93)( 22,106)( 23,112)( 24,111)( 25,110)( 26,109)( 27,108)( 28,107)( 29,120)( 30,126)( 31,125)( 32,124)( 33,123)( 34,122)( 35,121)( 36,113)( 37,119)( 38,118)( 39,117)( 40,116)( 41,115)( 42,114)( 43,148)( 44,154)( 45,153)( 46,152)( 47,151)( 48,150)( 49,149)( 50,162)( 51,168)( 52,167)( 53,166)( 54,165)( 55,164)( 56,163)( 57,155)( 58,161)( 59,160)( 60,159)( 61,158)( 62,157)( 63,156)( 64,127)( 65,133)( 66,132)( 67,131)( 68,130)( 69,129)( 70,128)( 71,141)( 72,147)( 73,146)( 74,145)( 75,144)( 76,143)( 77,142)( 78,134)( 79,140)( 80,139)( 81,138)( 82,137)( 83,136)( 84,135);; s2 := ( 1, 9)( 2, 8)( 3, 14)( 4, 13)( 5, 12)( 6, 11)( 7, 10)( 15, 16)( 17, 21)( 18, 20)( 22, 30)( 23, 29)( 24, 35)( 25, 34)( 26, 33)( 27, 32)( 28, 31)( 36, 37)( 38, 42)( 39, 41)( 43, 51)( 44, 50)( 45, 56)( 46, 55)( 47, 54)( 48, 53)( 49, 52)( 57, 58)( 59, 63)( 60, 62)( 64, 72)( 65, 71)( 66, 77)( 67, 76)( 68, 75)( 69, 74)( 70, 73)( 78, 79)( 80, 84)( 81, 83)( 85, 93)( 86, 92)( 87, 98)( 88, 97)( 89, 96)( 90, 95)( 91, 94)( 99,100)(101,105)(102,104)(106,114)(107,113)(108,119)(109,118)(110,117)(111,116)(112,115)(120,121)(122,126)(123,125)(127,135)(128,134)(129,140)(130,139)(131,138)(132,137)(133,136)(141,142)(143,147)(144,146)(148,156)(149,155)(150,161)(151,160)(152,159)(153,158)(154,157)(162,163)(164,168)(165,167);; s3 := (169,170);; 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, s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*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*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(170)!( 43, 64)( 44, 65)( 45, 66)( 46, 67)( 47, 68)( 48, 69)( 49, 70)( 50, 71)( 51, 72)( 52, 73)( 53, 74)( 54, 75)( 55, 76)( 56, 77)( 57, 78)( 58, 79)( 59, 80)( 60, 81)( 61, 82)( 62, 83)( 63, 84)( 85,127)( 86,128)( 87,129)( 88,130)( 89,131)( 90,132)( 91,133)( 92,134)( 93,135)( 94,136)( 95,137)( 96,138)( 97,139)( 98,140)( 99,141)(100,142)(101,143)(102,144)(103,145)(104,146)(105,147)(106,148)(107,149)(108,150)(109,151)(110,152)(111,153)(112,154)(113,155)(114,156)(115,157)(116,158)(117,159)(118,160)(119,161)(120,162)(121,163)(122,164)(123,165)(124,166)(125,167)(126,168); s1 := Sym(170)!( 1, 85)( 2, 91)( 3, 90)( 4, 89)( 5, 88)( 6, 87)( 7, 86)( 8, 99)( 9,105)( 10,104)( 11,103)( 12,102)( 13,101)( 14,100)( 15, 92)( 16, 98)( 17, 97)( 18, 96)( 19, 95)( 20, 94)( 21, 93)( 22,106)( 23,112)( 24,111)( 25,110)( 26,109)( 27,108)( 28,107)( 29,120)( 30,126)( 31,125)( 32,124)( 33,123)( 34,122)( 35,121)( 36,113)( 37,119)( 38,118)( 39,117)( 40,116)( 41,115)( 42,114)( 43,148)( 44,154)( 45,153)( 46,152)( 47,151)( 48,150)( 49,149)( 50,162)( 51,168)( 52,167)( 53,166)( 54,165)( 55,164)( 56,163)( 57,155)( 58,161)( 59,160)( 60,159)( 61,158)( 62,157)( 63,156)( 64,127)( 65,133)( 66,132)( 67,131)( 68,130)( 69,129)( 70,128)( 71,141)( 72,147)( 73,146)( 74,145)( 75,144)( 76,143)( 77,142)( 78,134)( 79,140)( 80,139)( 81,138)( 82,137)( 83,136)( 84,135); s2 := Sym(170)!( 1, 9)( 2, 8)( 3, 14)( 4, 13)( 5, 12)( 6, 11)( 7, 10)( 15, 16)( 17, 21)( 18, 20)( 22, 30)( 23, 29)( 24, 35)( 25, 34)( 26, 33)( 27, 32)( 28, 31)( 36, 37)( 38, 42)( 39, 41)( 43, 51)( 44, 50)( 45, 56)( 46, 55)( 47, 54)( 48, 53)( 49, 52)( 57, 58)( 59, 63)( 60, 62)( 64, 72)( 65, 71)( 66, 77)( 67, 76)( 68, 75)( 69, 74)( 70, 73)( 78, 79)( 80, 84)( 81, 83)( 85, 93)( 86, 92)( 87, 98)( 88, 97)( 89, 96)( 90, 95)( 91, 94)( 99,100)(101,105)(102,104)(106,114)(107,113)(108,119)(109,118)(110,117)(111,116)(112,115)(120,121)(122,126)(123,125)(127,135)(128,134)(129,140)(130,139)(131,138)(132,137)(133,136)(141,142)(143,147)(144,146)(148,156)(149,155)(150,161)(151,160)(152,159)(153,158)(154,157)(162,163)(164,168)(165,167); s3 := Sym(170)!(169,170); poly := sub<Sym(170)|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, s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*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*s1*s2*s1*s2*s1*s2*s1*s2 >;