Overview
- Group
- SmallGroup(928,131)
- Rank
- 3
- Schläfli Type
- {8,58}
- Vertices, edges, …
- 8, 232, 58
- Order of s0s1s2
- 232
- Order of s0s1s2s1
- 2
- Also known as
- {8,58|2}. if this polytope has another name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
4-fold
8-fold
29-fold
58-fold
116-fold
Covers minimal covers in bold
2-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 59, 88)( 60, 89)( 61, 90)( 62, 91)( 63, 92)( 64, 93)( 65, 94)( 66, 95)( 67, 96)( 68, 97)( 69, 98)( 70, 99)( 71,100)( 72,101)( 73,102)( 74,103)( 75,104)( 76,105)( 77,106)( 78,107)( 79,108)( 80,109)( 81,110)( 82,111)( 83,112)( 84,113)( 85,114)( 86,115)( 87,116)(117,175)(118,176)(119,177)(120,178)(121,179)(122,180)(123,181)(124,182)(125,183)(126,184)(127,185)(128,186)(129,187)(130,188)(131,189)(132,190)(133,191)(134,192)(135,193)(136,194)(137,195)(138,196)(139,197)(140,198)(141,199)(142,200)(143,201)(144,202)(145,203)(146,204)(147,205)(148,206)(149,207)(150,208)(151,209)(152,210)(153,211)(154,212)(155,213)(156,214)(157,215)(158,216)(159,217)(160,218)(161,219)(162,220)(163,221)(164,222)(165,223)(166,224)(167,225)(168,226)(169,227)(170,228)(171,229)(172,230)(173,231)(174,232);; s1 := ( 1,117)( 2,145)( 3,144)( 4,143)( 5,142)( 6,141)( 7,140)( 8,139)( 9,138)( 10,137)( 11,136)( 12,135)( 13,134)( 14,133)( 15,132)( 16,131)( 17,130)( 18,129)( 19,128)( 20,127)( 21,126)( 22,125)( 23,124)( 24,123)( 25,122)( 26,121)( 27,120)( 28,119)( 29,118)( 30,146)( 31,174)( 32,173)( 33,172)( 34,171)( 35,170)( 36,169)( 37,168)( 38,167)( 39,166)( 40,165)( 41,164)( 42,163)( 43,162)( 44,161)( 45,160)( 46,159)( 47,158)( 48,157)( 49,156)( 50,155)( 51,154)( 52,153)( 53,152)( 54,151)( 55,150)( 56,149)( 57,148)( 58,147)( 59,204)( 60,232)( 61,231)( 62,230)( 63,229)( 64,228)( 65,227)( 66,226)( 67,225)( 68,224)( 69,223)( 70,222)( 71,221)( 72,220)( 73,219)( 74,218)( 75,217)( 76,216)( 77,215)( 78,214)( 79,213)( 80,212)( 81,211)( 82,210)( 83,209)( 84,208)( 85,207)( 86,206)( 87,205)( 88,175)( 89,203)( 90,202)( 91,201)( 92,200)( 93,199)( 94,198)( 95,197)( 96,196)( 97,195)( 98,194)( 99,193)(100,192)(101,191)(102,190)(103,189)(104,188)(105,187)(106,186)(107,185)(108,184)(109,183)(110,182)(111,181)(112,180)(113,179)(114,178)(115,177)(116,176);; s2 := ( 1, 2)( 3, 29)( 4, 28)( 5, 27)( 6, 26)( 7, 25)( 8, 24)( 9, 23)( 10, 22)( 11, 21)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 30, 31)( 32, 58)( 33, 57)( 34, 56)( 35, 55)( 36, 54)( 37, 53)( 38, 52)( 39, 51)( 40, 50)( 41, 49)( 42, 48)( 43, 47)( 44, 46)( 59, 60)( 61, 87)( 62, 86)( 63, 85)( 64, 84)( 65, 83)( 66, 82)( 67, 81)( 68, 80)( 69, 79)( 70, 78)( 71, 77)( 72, 76)( 73, 75)( 88, 89)( 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)(117,118)(119,145)(120,144)(121,143)(122,142)(123,141)(124,140)(125,139)(126,138)(127,137)(128,136)(129,135)(130,134)(131,133)(146,147)(148,174)(149,173)(150,172)(151,171)(152,170)(153,169)(154,168)(155,167)(156,166)(157,165)(158,164)(159,163)(160,162)(175,176)(177,203)(178,202)(179,201)(180,200)(181,199)(182,198)(183,197)(184,196)(185,195)(186,194)(187,193)(188,192)(189,191)(204,205)(206,232)(207,231)(208,230)(209,229)(210,228)(211,227)(212,226)(213,225)(214,224)(215,223)(216,222)(217,221)(218,220);; poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, 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*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(232)!( 59, 88)( 60, 89)( 61, 90)( 62, 91)( 63, 92)( 64, 93)( 65, 94)( 66, 95)( 67, 96)( 68, 97)( 69, 98)( 70, 99)( 71,100)( 72,101)( 73,102)( 74,103)( 75,104)( 76,105)( 77,106)( 78,107)( 79,108)( 80,109)( 81,110)( 82,111)( 83,112)( 84,113)( 85,114)( 86,115)( 87,116)(117,175)(118,176)(119,177)(120,178)(121,179)(122,180)(123,181)(124,182)(125,183)(126,184)(127,185)(128,186)(129,187)(130,188)(131,189)(132,190)(133,191)(134,192)(135,193)(136,194)(137,195)(138,196)(139,197)(140,198)(141,199)(142,200)(143,201)(144,202)(145,203)(146,204)(147,205)(148,206)(149,207)(150,208)(151,209)(152,210)(153,211)(154,212)(155,213)(156,214)(157,215)(158,216)(159,217)(160,218)(161,219)(162,220)(163,221)(164,222)(165,223)(166,224)(167,225)(168,226)(169,227)(170,228)(171,229)(172,230)(173,231)(174,232); s1 := Sym(232)!( 1,117)( 2,145)( 3,144)( 4,143)( 5,142)( 6,141)( 7,140)( 8,139)( 9,138)( 10,137)( 11,136)( 12,135)( 13,134)( 14,133)( 15,132)( 16,131)( 17,130)( 18,129)( 19,128)( 20,127)( 21,126)( 22,125)( 23,124)( 24,123)( 25,122)( 26,121)( 27,120)( 28,119)( 29,118)( 30,146)( 31,174)( 32,173)( 33,172)( 34,171)( 35,170)( 36,169)( 37,168)( 38,167)( 39,166)( 40,165)( 41,164)( 42,163)( 43,162)( 44,161)( 45,160)( 46,159)( 47,158)( 48,157)( 49,156)( 50,155)( 51,154)( 52,153)( 53,152)( 54,151)( 55,150)( 56,149)( 57,148)( 58,147)( 59,204)( 60,232)( 61,231)( 62,230)( 63,229)( 64,228)( 65,227)( 66,226)( 67,225)( 68,224)( 69,223)( 70,222)( 71,221)( 72,220)( 73,219)( 74,218)( 75,217)( 76,216)( 77,215)( 78,214)( 79,213)( 80,212)( 81,211)( 82,210)( 83,209)( 84,208)( 85,207)( 86,206)( 87,205)( 88,175)( 89,203)( 90,202)( 91,201)( 92,200)( 93,199)( 94,198)( 95,197)( 96,196)( 97,195)( 98,194)( 99,193)(100,192)(101,191)(102,190)(103,189)(104,188)(105,187)(106,186)(107,185)(108,184)(109,183)(110,182)(111,181)(112,180)(113,179)(114,178)(115,177)(116,176); s2 := Sym(232)!( 1, 2)( 3, 29)( 4, 28)( 5, 27)( 6, 26)( 7, 25)( 8, 24)( 9, 23)( 10, 22)( 11, 21)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 30, 31)( 32, 58)( 33, 57)( 34, 56)( 35, 55)( 36, 54)( 37, 53)( 38, 52)( 39, 51)( 40, 50)( 41, 49)( 42, 48)( 43, 47)( 44, 46)( 59, 60)( 61, 87)( 62, 86)( 63, 85)( 64, 84)( 65, 83)( 66, 82)( 67, 81)( 68, 80)( 69, 79)( 70, 78)( 71, 77)( 72, 76)( 73, 75)( 88, 89)( 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)(117,118)(119,145)(120,144)(121,143)(122,142)(123,141)(124,140)(125,139)(126,138)(127,137)(128,136)(129,135)(130,134)(131,133)(146,147)(148,174)(149,173)(150,172)(151,171)(152,170)(153,169)(154,168)(155,167)(156,166)(157,165)(158,164)(159,163)(160,162)(175,176)(177,203)(178,202)(179,201)(180,200)(181,199)(182,198)(183,197)(184,196)(185,195)(186,194)(187,193)(188,192)(189,191)(204,205)(206,232)(207,231)(208,230)(209,229)(210,228)(211,227)(212,226)(213,225)(214,224)(215,223)(216,222)(217,221)(218,220); poly := sub<Sym(232)|s0,s1,s2>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, 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*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 >;
References
None.
to this polytope.