Overview
- Group
- SmallGroup(1360,241)
- Rank
- 4
- Schläfli Type
- {10,34,2}
- Vertices, edges, …
- 10, 170, 34, 2
- Order of s0s1s2s3
- 170
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
5-fold
10-fold
17-fold
34-fold
85-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 18, 69)( 19, 70)( 20, 71)( 21, 72)( 22, 73)( 23, 74)( 24, 75)( 25, 76)( 26, 77)( 27, 78)( 28, 79)( 29, 80)( 30, 81)( 31, 82)( 32, 83)( 33, 84)( 34, 85)( 35, 52)( 36, 53)( 37, 54)( 38, 55)( 39, 56)( 40, 57)( 41, 58)( 42, 59)( 43, 60)( 44, 61)( 45, 62)( 46, 63)( 47, 64)( 48, 65)( 49, 66)( 50, 67)( 51, 68)(103,154)(104,155)(105,156)(106,157)(107,158)(108,159)(109,160)(110,161)(111,162)(112,163)(113,164)(114,165)(115,166)(116,167)(117,168)(118,169)(119,170)(120,137)(121,138)(122,139)(123,140)(124,141)(125,142)(126,143)(127,144)(128,145)(129,146)(130,147)(131,148)(132,149)(133,150)(134,151)(135,152)(136,153);; s1 := ( 1, 18)( 2, 34)( 3, 33)( 4, 32)( 5, 31)( 6, 30)( 7, 29)( 8, 28)( 9, 27)( 10, 26)( 11, 25)( 12, 24)( 13, 23)( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 35, 69)( 36, 85)( 37, 84)( 38, 83)( 39, 82)( 40, 81)( 41, 80)( 42, 79)( 43, 78)( 44, 77)( 45, 76)( 46, 75)( 47, 74)( 48, 73)( 49, 72)( 50, 71)( 51, 70)( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)( 59, 62)( 60, 61)( 86,103)( 87,119)( 88,118)( 89,117)( 90,116)( 91,115)( 92,114)( 93,113)( 94,112)( 95,111)( 96,110)( 97,109)( 98,108)( 99,107)(100,106)(101,105)(102,104)(120,154)(121,170)(122,169)(123,168)(124,167)(125,166)(126,165)(127,164)(128,163)(129,162)(130,161)(131,160)(132,159)(133,158)(134,157)(135,156)(136,155)(138,153)(139,152)(140,151)(141,150)(142,149)(143,148)(144,147)(145,146);; s2 := ( 1, 87)( 2, 86)( 3,102)( 4,101)( 5,100)( 6, 99)( 7, 98)( 8, 97)( 9, 96)( 10, 95)( 11, 94)( 12, 93)( 13, 92)( 14, 91)( 15, 90)( 16, 89)( 17, 88)( 18,104)( 19,103)( 20,119)( 21,118)( 22,117)( 23,116)( 24,115)( 25,114)( 26,113)( 27,112)( 28,111)( 29,110)( 30,109)( 31,108)( 32,107)( 33,106)( 34,105)( 35,121)( 36,120)( 37,136)( 38,135)( 39,134)( 40,133)( 41,132)( 42,131)( 43,130)( 44,129)( 45,128)( 46,127)( 47,126)( 48,125)( 49,124)( 50,123)( 51,122)( 52,138)( 53,137)( 54,153)( 55,152)( 56,151)( 57,150)( 58,149)( 59,148)( 60,147)( 61,146)( 62,145)( 63,144)( 64,143)( 65,142)( 66,141)( 67,140)( 68,139)( 69,155)( 70,154)( 71,170)( 72,169)( 73,168)( 74,167)( 75,166)( 76,165)( 77,164)( 78,163)( 79,162)( 80,161)( 81,160)( 82,159)( 83,158)( 84,157)( 85,156);; s3 := (171,172);; 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*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(172)!( 18, 69)( 19, 70)( 20, 71)( 21, 72)( 22, 73)( 23, 74)( 24, 75)( 25, 76)( 26, 77)( 27, 78)( 28, 79)( 29, 80)( 30, 81)( 31, 82)( 32, 83)( 33, 84)( 34, 85)( 35, 52)( 36, 53)( 37, 54)( 38, 55)( 39, 56)( 40, 57)( 41, 58)( 42, 59)( 43, 60)( 44, 61)( 45, 62)( 46, 63)( 47, 64)( 48, 65)( 49, 66)( 50, 67)( 51, 68)(103,154)(104,155)(105,156)(106,157)(107,158)(108,159)(109,160)(110,161)(111,162)(112,163)(113,164)(114,165)(115,166)(116,167)(117,168)(118,169)(119,170)(120,137)(121,138)(122,139)(123,140)(124,141)(125,142)(126,143)(127,144)(128,145)(129,146)(130,147)(131,148)(132,149)(133,150)(134,151)(135,152)(136,153); s1 := Sym(172)!( 1, 18)( 2, 34)( 3, 33)( 4, 32)( 5, 31)( 6, 30)( 7, 29)( 8, 28)( 9, 27)( 10, 26)( 11, 25)( 12, 24)( 13, 23)( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 35, 69)( 36, 85)( 37, 84)( 38, 83)( 39, 82)( 40, 81)( 41, 80)( 42, 79)( 43, 78)( 44, 77)( 45, 76)( 46, 75)( 47, 74)( 48, 73)( 49, 72)( 50, 71)( 51, 70)( 53, 68)( 54, 67)( 55, 66)( 56, 65)( 57, 64)( 58, 63)( 59, 62)( 60, 61)( 86,103)( 87,119)( 88,118)( 89,117)( 90,116)( 91,115)( 92,114)( 93,113)( 94,112)( 95,111)( 96,110)( 97,109)( 98,108)( 99,107)(100,106)(101,105)(102,104)(120,154)(121,170)(122,169)(123,168)(124,167)(125,166)(126,165)(127,164)(128,163)(129,162)(130,161)(131,160)(132,159)(133,158)(134,157)(135,156)(136,155)(138,153)(139,152)(140,151)(141,150)(142,149)(143,148)(144,147)(145,146); s2 := Sym(172)!( 1, 87)( 2, 86)( 3,102)( 4,101)( 5,100)( 6, 99)( 7, 98)( 8, 97)( 9, 96)( 10, 95)( 11, 94)( 12, 93)( 13, 92)( 14, 91)( 15, 90)( 16, 89)( 17, 88)( 18,104)( 19,103)( 20,119)( 21,118)( 22,117)( 23,116)( 24,115)( 25,114)( 26,113)( 27,112)( 28,111)( 29,110)( 30,109)( 31,108)( 32,107)( 33,106)( 34,105)( 35,121)( 36,120)( 37,136)( 38,135)( 39,134)( 40,133)( 41,132)( 42,131)( 43,130)( 44,129)( 45,128)( 46,127)( 47,126)( 48,125)( 49,124)( 50,123)( 51,122)( 52,138)( 53,137)( 54,153)( 55,152)( 56,151)( 57,150)( 58,149)( 59,148)( 60,147)( 61,146)( 62,145)( 63,144)( 64,143)( 65,142)( 66,141)( 67,140)( 68,139)( 69,155)( 70,154)( 71,170)( 72,169)( 73,168)( 74,167)( 75,166)( 76,165)( 77,164)( 78,163)( 79,162)( 80,161)( 81,160)( 82,159)( 83,158)( 84,157)( 85,156); s3 := Sym(172)!(171,172); poly := sub<Sym(172)|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*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 >;