Overview
- Group
- SmallGroup(1456,175)
- Rank
- 4
- Schläfli Type
- {2,14,26}
- Vertices, edges, …
- 2, 14, 182, 26
- Order of s0s1s2s3
- 182
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
7-fold
13-fold
14-fold
26-fold
91-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 16, 81)( 17, 82)( 18, 83)( 19, 84)( 20, 85)( 21, 86)( 22, 87)( 23, 88)( 24, 89)( 25, 90)( 26, 91)( 27, 92)( 28, 93)( 29, 68)( 30, 69)( 31, 70)( 32, 71)( 33, 72)( 34, 73)( 35, 74)( 36, 75)( 37, 76)( 38, 77)( 39, 78)( 40, 79)( 41, 80)( 42, 55)( 43, 56)( 44, 57)( 45, 58)( 46, 59)( 47, 60)( 48, 61)( 49, 62)( 50, 63)( 51, 64)( 52, 65)( 53, 66)( 54, 67)(107,172)(108,173)(109,174)(110,175)(111,176)(112,177)(113,178)(114,179)(115,180)(116,181)(117,182)(118,183)(119,184)(120,159)(121,160)(122,161)(123,162)(124,163)(125,164)(126,165)(127,166)(128,167)(129,168)(130,169)(131,170)(132,171)(133,146)(134,147)(135,148)(136,149)(137,150)(138,151)(139,152)(140,153)(141,154)(142,155)(143,156)(144,157)(145,158);; s2 := ( 3, 16)( 4, 28)( 5, 27)( 6, 26)( 7, 25)( 8, 24)( 9, 23)( 10, 22)( 11, 21)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 29, 81)( 30, 93)( 31, 92)( 32, 91)( 33, 90)( 34, 89)( 35, 88)( 36, 87)( 37, 86)( 38, 85)( 39, 84)( 40, 83)( 41, 82)( 42, 68)( 43, 80)( 44, 79)( 45, 78)( 46, 77)( 47, 76)( 48, 75)( 49, 74)( 50, 73)( 51, 72)( 52, 71)( 53, 70)( 54, 69)( 56, 67)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 94,107)( 95,119)( 96,118)( 97,117)( 98,116)( 99,115)(100,114)(101,113)(102,112)(103,111)(104,110)(105,109)(106,108)(120,172)(121,184)(122,183)(123,182)(124,181)(125,180)(126,179)(127,178)(128,177)(129,176)(130,175)(131,174)(132,173)(133,159)(134,171)(135,170)(136,169)(137,168)(138,167)(139,166)(140,165)(141,164)(142,163)(143,162)(144,161)(145,160)(147,158)(148,157)(149,156)(150,155)(151,154)(152,153);; s3 := ( 3, 95)( 4, 94)( 5,106)( 6,105)( 7,104)( 8,103)( 9,102)( 10,101)( 11,100)( 12, 99)( 13, 98)( 14, 97)( 15, 96)( 16,108)( 17,107)( 18,119)( 19,118)( 20,117)( 21,116)( 22,115)( 23,114)( 24,113)( 25,112)( 26,111)( 27,110)( 28,109)( 29,121)( 30,120)( 31,132)( 32,131)( 33,130)( 34,129)( 35,128)( 36,127)( 37,126)( 38,125)( 39,124)( 40,123)( 41,122)( 42,134)( 43,133)( 44,145)( 45,144)( 46,143)( 47,142)( 48,141)( 49,140)( 50,139)( 51,138)( 52,137)( 53,136)( 54,135)( 55,147)( 56,146)( 57,158)( 58,157)( 59,156)( 60,155)( 61,154)( 62,153)( 63,152)( 64,151)( 65,150)( 66,149)( 67,148)( 68,160)( 69,159)( 70,171)( 71,170)( 72,169)( 73,168)( 74,167)( 75,166)( 76,165)( 77,164)( 78,163)( 79,162)( 80,161)( 81,173)( 82,172)( 83,184)( 84,183)( 85,182)( 86,181)( 87,180)( 88,179)( 89,178)( 90,177)( 91,176)( 92,175)( 93,174);; 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, 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,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(184)!(1,2); s1 := Sym(184)!( 16, 81)( 17, 82)( 18, 83)( 19, 84)( 20, 85)( 21, 86)( 22, 87)( 23, 88)( 24, 89)( 25, 90)( 26, 91)( 27, 92)( 28, 93)( 29, 68)( 30, 69)( 31, 70)( 32, 71)( 33, 72)( 34, 73)( 35, 74)( 36, 75)( 37, 76)( 38, 77)( 39, 78)( 40, 79)( 41, 80)( 42, 55)( 43, 56)( 44, 57)( 45, 58)( 46, 59)( 47, 60)( 48, 61)( 49, 62)( 50, 63)( 51, 64)( 52, 65)( 53, 66)( 54, 67)(107,172)(108,173)(109,174)(110,175)(111,176)(112,177)(113,178)(114,179)(115,180)(116,181)(117,182)(118,183)(119,184)(120,159)(121,160)(122,161)(123,162)(124,163)(125,164)(126,165)(127,166)(128,167)(129,168)(130,169)(131,170)(132,171)(133,146)(134,147)(135,148)(136,149)(137,150)(138,151)(139,152)(140,153)(141,154)(142,155)(143,156)(144,157)(145,158); s2 := Sym(184)!( 3, 16)( 4, 28)( 5, 27)( 6, 26)( 7, 25)( 8, 24)( 9, 23)( 10, 22)( 11, 21)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 29, 81)( 30, 93)( 31, 92)( 32, 91)( 33, 90)( 34, 89)( 35, 88)( 36, 87)( 37, 86)( 38, 85)( 39, 84)( 40, 83)( 41, 82)( 42, 68)( 43, 80)( 44, 79)( 45, 78)( 46, 77)( 47, 76)( 48, 75)( 49, 74)( 50, 73)( 51, 72)( 52, 71)( 53, 70)( 54, 69)( 56, 67)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 94,107)( 95,119)( 96,118)( 97,117)( 98,116)( 99,115)(100,114)(101,113)(102,112)(103,111)(104,110)(105,109)(106,108)(120,172)(121,184)(122,183)(123,182)(124,181)(125,180)(126,179)(127,178)(128,177)(129,176)(130,175)(131,174)(132,173)(133,159)(134,171)(135,170)(136,169)(137,168)(138,167)(139,166)(140,165)(141,164)(142,163)(143,162)(144,161)(145,160)(147,158)(148,157)(149,156)(150,155)(151,154)(152,153); s3 := Sym(184)!( 3, 95)( 4, 94)( 5,106)( 6,105)( 7,104)( 8,103)( 9,102)( 10,101)( 11,100)( 12, 99)( 13, 98)( 14, 97)( 15, 96)( 16,108)( 17,107)( 18,119)( 19,118)( 20,117)( 21,116)( 22,115)( 23,114)( 24,113)( 25,112)( 26,111)( 27,110)( 28,109)( 29,121)( 30,120)( 31,132)( 32,131)( 33,130)( 34,129)( 35,128)( 36,127)( 37,126)( 38,125)( 39,124)( 40,123)( 41,122)( 42,134)( 43,133)( 44,145)( 45,144)( 46,143)( 47,142)( 48,141)( 49,140)( 50,139)( 51,138)( 52,137)( 53,136)( 54,135)( 55,147)( 56,146)( 57,158)( 58,157)( 59,156)( 60,155)( 61,154)( 62,153)( 63,152)( 64,151)( 65,150)( 66,149)( 67,148)( 68,160)( 69,159)( 70,171)( 71,170)( 72,169)( 73,168)( 74,167)( 75,166)( 76,165)( 77,164)( 78,163)( 79,162)( 80,161)( 81,173)( 82,172)( 83,184)( 84,183)( 85,182)( 86,181)( 87,180)( 88,179)( 89,178)( 90,177)( 91,176)( 92,175)( 93,174); poly := sub<Sym(184)|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, 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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;