Overview
- Group
- SmallGroup(1360,241)
- Rank
- 4
- Schläfli Type
- {2,34,10}
- Vertices, edges, …
- 2, 34, 170, 10
- 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 := (1,2);; s1 := ( 4, 19)( 5, 18)( 6, 17)( 7, 16)( 8, 15)( 9, 14)( 10, 13)( 11, 12)( 21, 36)( 22, 35)( 23, 34)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)( 38, 53)( 39, 52)( 40, 51)( 41, 50)( 42, 49)( 43, 48)( 44, 47)( 45, 46)( 55, 70)( 56, 69)( 57, 68)( 58, 67)( 59, 66)( 60, 65)( 61, 64)( 62, 63)( 72, 87)( 73, 86)( 74, 85)( 75, 84)( 76, 83)( 77, 82)( 78, 81)( 79, 80)( 89,104)( 90,103)( 91,102)( 92,101)( 93,100)( 94, 99)( 95, 98)( 96, 97)(106,121)(107,120)(108,119)(109,118)(110,117)(111,116)(112,115)(113,114)(123,138)(124,137)(125,136)(126,135)(127,134)(128,133)(129,132)(130,131)(140,155)(141,154)(142,153)(143,152)(144,151)(145,150)(146,149)(147,148)(157,172)(158,171)(159,170)(160,169)(161,168)(162,167)(163,166)(164,165);; s2 := ( 3, 4)( 5, 19)( 6, 18)( 7, 17)( 8, 16)( 9, 15)( 10, 14)( 11, 13)( 20, 72)( 21, 71)( 22, 87)( 23, 86)( 24, 85)( 25, 84)( 26, 83)( 27, 82)( 28, 81)( 29, 80)( 30, 79)( 31, 78)( 32, 77)( 33, 76)( 34, 75)( 35, 74)( 36, 73)( 37, 55)( 38, 54)( 39, 70)( 40, 69)( 41, 68)( 42, 67)( 43, 66)( 44, 65)( 45, 64)( 46, 63)( 47, 62)( 48, 61)( 49, 60)( 50, 59)( 51, 58)( 52, 57)( 53, 56)( 88, 89)( 90,104)( 91,103)( 92,102)( 93,101)( 94,100)( 95, 99)( 96, 98)(105,157)(106,156)(107,172)(108,171)(109,170)(110,169)(111,168)(112,167)(113,166)(114,165)(115,164)(116,163)(117,162)(118,161)(119,160)(120,159)(121,158)(122,140)(123,139)(124,155)(125,154)(126,153)(127,152)(128,151)(129,150)(130,149)(131,148)(132,147)(133,146)(134,145)(135,144)(136,143)(137,142)(138,141);; s3 := ( 3,105)( 4,106)( 5,107)( 6,108)( 7,109)( 8,110)( 9,111)( 10,112)( 11,113)( 12,114)( 13,115)( 14,116)( 15,117)( 16,118)( 17,119)( 18,120)( 19,121)( 20, 88)( 21, 89)( 22, 90)( 23, 91)( 24, 92)( 25, 93)( 26, 94)( 27, 95)( 28, 96)( 29, 97)( 30, 98)( 31, 99)( 32,100)( 33,101)( 34,102)( 35,103)( 36,104)( 37,156)( 38,157)( 39,158)( 40,159)( 41,160)( 42,161)( 43,162)( 44,163)( 45,164)( 46,165)( 47,166)( 48,167)( 49,168)( 50,169)( 51,170)( 52,171)( 53,172)( 54,139)( 55,140)( 56,141)( 57,142)( 58,143)( 59,144)( 60,145)( 61,146)( 62,147)( 63,148)( 64,149)( 65,150)( 66,151)( 67,152)( 68,153)( 69,154)( 70,155)( 71,122)( 72,123)( 73,124)( 74,125)( 75,126)( 76,127)( 77,128)( 78,129)( 79,130)( 80,131)( 81,132)( 82,133)( 83,134)( 84,135)( 85,136)( 86,137)( 87,138);; 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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*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*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)!(1,2); s1 := Sym(172)!( 4, 19)( 5, 18)( 6, 17)( 7, 16)( 8, 15)( 9, 14)( 10, 13)( 11, 12)( 21, 36)( 22, 35)( 23, 34)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)( 38, 53)( 39, 52)( 40, 51)( 41, 50)( 42, 49)( 43, 48)( 44, 47)( 45, 46)( 55, 70)( 56, 69)( 57, 68)( 58, 67)( 59, 66)( 60, 65)( 61, 64)( 62, 63)( 72, 87)( 73, 86)( 74, 85)( 75, 84)( 76, 83)( 77, 82)( 78, 81)( 79, 80)( 89,104)( 90,103)( 91,102)( 92,101)( 93,100)( 94, 99)( 95, 98)( 96, 97)(106,121)(107,120)(108,119)(109,118)(110,117)(111,116)(112,115)(113,114)(123,138)(124,137)(125,136)(126,135)(127,134)(128,133)(129,132)(130,131)(140,155)(141,154)(142,153)(143,152)(144,151)(145,150)(146,149)(147,148)(157,172)(158,171)(159,170)(160,169)(161,168)(162,167)(163,166)(164,165); s2 := Sym(172)!( 3, 4)( 5, 19)( 6, 18)( 7, 17)( 8, 16)( 9, 15)( 10, 14)( 11, 13)( 20, 72)( 21, 71)( 22, 87)( 23, 86)( 24, 85)( 25, 84)( 26, 83)( 27, 82)( 28, 81)( 29, 80)( 30, 79)( 31, 78)( 32, 77)( 33, 76)( 34, 75)( 35, 74)( 36, 73)( 37, 55)( 38, 54)( 39, 70)( 40, 69)( 41, 68)( 42, 67)( 43, 66)( 44, 65)( 45, 64)( 46, 63)( 47, 62)( 48, 61)( 49, 60)( 50, 59)( 51, 58)( 52, 57)( 53, 56)( 88, 89)( 90,104)( 91,103)( 92,102)( 93,101)( 94,100)( 95, 99)( 96, 98)(105,157)(106,156)(107,172)(108,171)(109,170)(110,169)(111,168)(112,167)(113,166)(114,165)(115,164)(116,163)(117,162)(118,161)(119,160)(120,159)(121,158)(122,140)(123,139)(124,155)(125,154)(126,153)(127,152)(128,151)(129,150)(130,149)(131,148)(132,147)(133,146)(134,145)(135,144)(136,143)(137,142)(138,141); s3 := Sym(172)!( 3,105)( 4,106)( 5,107)( 6,108)( 7,109)( 8,110)( 9,111)( 10,112)( 11,113)( 12,114)( 13,115)( 14,116)( 15,117)( 16,118)( 17,119)( 18,120)( 19,121)( 20, 88)( 21, 89)( 22, 90)( 23, 91)( 24, 92)( 25, 93)( 26, 94)( 27, 95)( 28, 96)( 29, 97)( 30, 98)( 31, 99)( 32,100)( 33,101)( 34,102)( 35,103)( 36,104)( 37,156)( 38,157)( 39,158)( 40,159)( 41,160)( 42,161)( 43,162)( 44,163)( 45,164)( 46,165)( 47,166)( 48,167)( 49,168)( 50,169)( 51,170)( 52,171)( 53,172)( 54,139)( 55,140)( 56,141)( 57,142)( 58,143)( 59,144)( 60,145)( 61,146)( 62,147)( 63,148)( 64,149)( 65,150)( 66,151)( 67,152)( 68,153)( 69,154)( 70,155)( 71,122)( 72,123)( 73,124)( 74,125)( 75,126)( 76,127)( 77,128)( 78,129)( 79,130)( 80,131)( 81,132)( 82,133)( 83,134)( 84,135)( 85,136)( 86,137)( 87,138); 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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;