Overview
- Group
- SmallGroup(1344,11695)
- Rank
- 5
- Schläfli Type
- {2,4,6,14}
- Vertices, edges, …
- 2, 4, 12, 42, 14
- Order of s0s1s2s3s4
- 42
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
7-fold
14-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 3, 5)( 4, 6)( 7, 9)( 8, 10)( 11, 13)( 12, 14)( 15, 17)( 16, 18)( 19, 21)( 20, 22)( 23, 25)( 24, 26)( 27, 29)( 28, 30)( 31, 33)( 32, 34)( 35, 37)( 36, 38)( 39, 41)( 40, 42)( 43, 45)( 44, 46)( 47, 49)( 48, 50)( 51, 53)( 52, 54)( 55, 57)( 56, 58)( 59, 61)( 60, 62)( 63, 65)( 64, 66)( 67, 69)( 68, 70)( 71, 73)( 72, 74)( 75, 77)( 76, 78)( 79, 81)( 80, 82)( 83, 85)( 84, 86)( 87, 89)( 88, 90)( 91, 93)( 92, 94)( 95, 97)( 96, 98)( 99,101)(100,102)(103,105)(104,106)(107,109)(108,110)(111,113)(112,114)(115,117)(116,118)(119,121)(120,122)(123,125)(124,126)(127,129)(128,130)(131,133)(132,134)(135,137)(136,138)(139,141)(140,142)(143,145)(144,146)(147,149)(148,150)(151,153)(152,154)(155,157)(156,158)(159,161)(160,162)(163,165)(164,166)(167,169)(168,170);; s2 := ( 4, 5)( 8, 9)( 12, 13)( 16, 17)( 20, 21)( 24, 25)( 28, 29)( 31, 59)( 32, 61)( 33, 60)( 34, 62)( 35, 63)( 36, 65)( 37, 64)( 38, 66)( 39, 67)( 40, 69)( 41, 68)( 42, 70)( 43, 71)( 44, 73)( 45, 72)( 46, 74)( 47, 75)( 48, 77)( 49, 76)( 50, 78)( 51, 79)( 52, 81)( 53, 80)( 54, 82)( 55, 83)( 56, 85)( 57, 84)( 58, 86)( 88, 89)( 92, 93)( 96, 97)(100,101)(104,105)(108,109)(112,113)(115,143)(116,145)(117,144)(118,146)(119,147)(120,149)(121,148)(122,150)(123,151)(124,153)(125,152)(126,154)(127,155)(128,157)(129,156)(130,158)(131,159)(132,161)(133,160)(134,162)(135,163)(136,165)(137,164)(138,166)(139,167)(140,169)(141,168)(142,170);; s3 := ( 3, 59)( 4, 62)( 5, 61)( 6, 60)( 7, 83)( 8, 86)( 9, 85)( 10, 84)( 11, 79)( 12, 82)( 13, 81)( 14, 80)( 15, 75)( 16, 78)( 17, 77)( 18, 76)( 19, 71)( 20, 74)( 21, 73)( 22, 72)( 23, 67)( 24, 70)( 25, 69)( 26, 68)( 27, 63)( 28, 66)( 29, 65)( 30, 64)( 32, 34)( 35, 55)( 36, 58)( 37, 57)( 38, 56)( 39, 51)( 40, 54)( 41, 53)( 42, 52)( 43, 47)( 44, 50)( 45, 49)( 46, 48)( 87,143)( 88,146)( 89,145)( 90,144)( 91,167)( 92,170)( 93,169)( 94,168)( 95,163)( 96,166)( 97,165)( 98,164)( 99,159)(100,162)(101,161)(102,160)(103,155)(104,158)(105,157)(106,156)(107,151)(108,154)(109,153)(110,152)(111,147)(112,150)(113,149)(114,148)(116,118)(119,139)(120,142)(121,141)(122,140)(123,135)(124,138)(125,137)(126,136)(127,131)(128,134)(129,133)(130,132);; s4 := ( 3, 91)( 4, 92)( 5, 93)( 6, 94)( 7, 87)( 8, 88)( 9, 89)( 10, 90)( 11,111)( 12,112)( 13,113)( 14,114)( 15,107)( 16,108)( 17,109)( 18,110)( 19,103)( 20,104)( 21,105)( 22,106)( 23, 99)( 24,100)( 25,101)( 26,102)( 27, 95)( 28, 96)( 29, 97)( 30, 98)( 31,119)( 32,120)( 33,121)( 34,122)( 35,115)( 36,116)( 37,117)( 38,118)( 39,139)( 40,140)( 41,141)( 42,142)( 43,135)( 44,136)( 45,137)( 46,138)( 47,131)( 48,132)( 49,133)( 50,134)( 51,127)( 52,128)( 53,129)( 54,130)( 55,123)( 56,124)( 57,125)( 58,126)( 59,147)( 60,148)( 61,149)( 62,150)( 63,143)( 64,144)( 65,145)( 66,146)( 67,167)( 68,168)( 69,169)( 70,170)( 71,163)( 72,164)( 73,165)( 74,166)( 75,159)( 76,160)( 77,161)( 78,162)( 79,155)( 80,156)( 81,157)( 82,158)( 83,151)( 84,152)( 85,153)( 86,154);; poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s4*s3*s2*s3*s4*s3,
s1*s2*s3*s2*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(170)!(1,2); s1 := Sym(170)!( 3, 5)( 4, 6)( 7, 9)( 8, 10)( 11, 13)( 12, 14)( 15, 17)( 16, 18)( 19, 21)( 20, 22)( 23, 25)( 24, 26)( 27, 29)( 28, 30)( 31, 33)( 32, 34)( 35, 37)( 36, 38)( 39, 41)( 40, 42)( 43, 45)( 44, 46)( 47, 49)( 48, 50)( 51, 53)( 52, 54)( 55, 57)( 56, 58)( 59, 61)( 60, 62)( 63, 65)( 64, 66)( 67, 69)( 68, 70)( 71, 73)( 72, 74)( 75, 77)( 76, 78)( 79, 81)( 80, 82)( 83, 85)( 84, 86)( 87, 89)( 88, 90)( 91, 93)( 92, 94)( 95, 97)( 96, 98)( 99,101)(100,102)(103,105)(104,106)(107,109)(108,110)(111,113)(112,114)(115,117)(116,118)(119,121)(120,122)(123,125)(124,126)(127,129)(128,130)(131,133)(132,134)(135,137)(136,138)(139,141)(140,142)(143,145)(144,146)(147,149)(148,150)(151,153)(152,154)(155,157)(156,158)(159,161)(160,162)(163,165)(164,166)(167,169)(168,170); s2 := Sym(170)!( 4, 5)( 8, 9)( 12, 13)( 16, 17)( 20, 21)( 24, 25)( 28, 29)( 31, 59)( 32, 61)( 33, 60)( 34, 62)( 35, 63)( 36, 65)( 37, 64)( 38, 66)( 39, 67)( 40, 69)( 41, 68)( 42, 70)( 43, 71)( 44, 73)( 45, 72)( 46, 74)( 47, 75)( 48, 77)( 49, 76)( 50, 78)( 51, 79)( 52, 81)( 53, 80)( 54, 82)( 55, 83)( 56, 85)( 57, 84)( 58, 86)( 88, 89)( 92, 93)( 96, 97)(100,101)(104,105)(108,109)(112,113)(115,143)(116,145)(117,144)(118,146)(119,147)(120,149)(121,148)(122,150)(123,151)(124,153)(125,152)(126,154)(127,155)(128,157)(129,156)(130,158)(131,159)(132,161)(133,160)(134,162)(135,163)(136,165)(137,164)(138,166)(139,167)(140,169)(141,168)(142,170); s3 := Sym(170)!( 3, 59)( 4, 62)( 5, 61)( 6, 60)( 7, 83)( 8, 86)( 9, 85)( 10, 84)( 11, 79)( 12, 82)( 13, 81)( 14, 80)( 15, 75)( 16, 78)( 17, 77)( 18, 76)( 19, 71)( 20, 74)( 21, 73)( 22, 72)( 23, 67)( 24, 70)( 25, 69)( 26, 68)( 27, 63)( 28, 66)( 29, 65)( 30, 64)( 32, 34)( 35, 55)( 36, 58)( 37, 57)( 38, 56)( 39, 51)( 40, 54)( 41, 53)( 42, 52)( 43, 47)( 44, 50)( 45, 49)( 46, 48)( 87,143)( 88,146)( 89,145)( 90,144)( 91,167)( 92,170)( 93,169)( 94,168)( 95,163)( 96,166)( 97,165)( 98,164)( 99,159)(100,162)(101,161)(102,160)(103,155)(104,158)(105,157)(106,156)(107,151)(108,154)(109,153)(110,152)(111,147)(112,150)(113,149)(114,148)(116,118)(119,139)(120,142)(121,141)(122,140)(123,135)(124,138)(125,137)(126,136)(127,131)(128,134)(129,133)(130,132); s4 := Sym(170)!( 3, 91)( 4, 92)( 5, 93)( 6, 94)( 7, 87)( 8, 88)( 9, 89)( 10, 90)( 11,111)( 12,112)( 13,113)( 14,114)( 15,107)( 16,108)( 17,109)( 18,110)( 19,103)( 20,104)( 21,105)( 22,106)( 23, 99)( 24,100)( 25,101)( 26,102)( 27, 95)( 28, 96)( 29, 97)( 30, 98)( 31,119)( 32,120)( 33,121)( 34,122)( 35,115)( 36,116)( 37,117)( 38,118)( 39,139)( 40,140)( 41,141)( 42,142)( 43,135)( 44,136)( 45,137)( 46,138)( 47,131)( 48,132)( 49,133)( 50,134)( 51,127)( 52,128)( 53,129)( 54,130)( 55,123)( 56,124)( 57,125)( 58,126)( 59,147)( 60,148)( 61,149)( 62,150)( 63,143)( 64,144)( 65,145)( 66,146)( 67,167)( 68,168)( 69,169)( 70,170)( 71,163)( 72,164)( 73,165)( 74,166)( 75,159)( 76,160)( 77,161)( 78,162)( 79,155)( 80,156)( 81,157)( 82,158)( 83,151)( 84,152)( 85,153)( 86,154); poly := sub<Sym(170)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s4*s3*s2*s3*s4*s3, s1*s2*s3*s2*s1*s2*s3*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;