Overview
- Group
- SmallGroup(864,126)
- Rank
- 3
- Schläfli Type
- {8,54}
- Vertices, edges, …
- 8, 216, 54
- Order of s0s1s2
- 216
- Order of s0s1s2s1
- 2
- Also known as
- {8,54|2}. if this polytope has another name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
8-fold
9-fold
12-fold
18-fold
24-fold
27-fold
36-fold
54-fold
72-fold
108-fold
Covers minimal covers in bold
2-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 55, 82)( 56, 83)( 57, 84)( 58, 85)( 59, 86)( 60, 87)( 61, 88)( 62, 89)( 63, 90)( 64, 91)( 65, 92)( 66, 93)( 67, 94)( 68, 95)( 69, 96)( 70, 97)( 71, 98)( 72, 99)( 73,100)( 74,101)( 75,102)( 76,103)( 77,104)( 78,105)( 79,106)( 80,107)( 81,108)(109,163)(110,164)(111,165)(112,166)(113,167)(114,168)(115,169)(116,170)(117,171)(118,172)(119,173)(120,174)(121,175)(122,176)(123,177)(124,178)(125,179)(126,180)(127,181)(128,182)(129,183)(130,184)(131,185)(132,186)(133,187)(134,188)(135,189)(136,190)(137,191)(138,192)(139,193)(140,194)(141,195)(142,196)(143,197)(144,198)(145,199)(146,200)(147,201)(148,202)(149,203)(150,204)(151,205)(152,206)(153,207)(154,208)(155,209)(156,210)(157,211)(158,212)(159,213)(160,214)(161,215)(162,216);; s1 := ( 1,109)( 2,111)( 3,110)( 4,117)( 5,116)( 6,115)( 7,114)( 8,113)( 9,112)( 10,135)( 11,134)( 12,133)( 13,132)( 14,131)( 15,130)( 16,129)( 17,128)( 18,127)( 19,126)( 20,125)( 21,124)( 22,123)( 23,122)( 24,121)( 25,120)( 26,119)( 27,118)( 28,136)( 29,138)( 30,137)( 31,144)( 32,143)( 33,142)( 34,141)( 35,140)( 36,139)( 37,162)( 38,161)( 39,160)( 40,159)( 41,158)( 42,157)( 43,156)( 44,155)( 45,154)( 46,153)( 47,152)( 48,151)( 49,150)( 50,149)( 51,148)( 52,147)( 53,146)( 54,145)( 55,190)( 56,192)( 57,191)( 58,198)( 59,197)( 60,196)( 61,195)( 62,194)( 63,193)( 64,216)( 65,215)( 66,214)( 67,213)( 68,212)( 69,211)( 70,210)( 71,209)( 72,208)( 73,207)( 74,206)( 75,205)( 76,204)( 77,203)( 78,202)( 79,201)( 80,200)( 81,199)( 82,163)( 83,165)( 84,164)( 85,171)( 86,170)( 87,169)( 88,168)( 89,167)( 90,166)( 91,189)( 92,188)( 93,187)( 94,186)( 95,185)( 96,184)( 97,183)( 98,182)( 99,181)(100,180)(101,179)(102,178)(103,177)(104,176)(105,175)(106,174)(107,173)(108,172);; s2 := ( 1, 10)( 2, 12)( 3, 11)( 4, 18)( 5, 17)( 6, 16)( 7, 15)( 8, 14)( 9, 13)( 19, 27)( 20, 26)( 21, 25)( 22, 24)( 28, 37)( 29, 39)( 30, 38)( 31, 45)( 32, 44)( 33, 43)( 34, 42)( 35, 41)( 36, 40)( 46, 54)( 47, 53)( 48, 52)( 49, 51)( 55, 64)( 56, 66)( 57, 65)( 58, 72)( 59, 71)( 60, 70)( 61, 69)( 62, 68)( 63, 67)( 73, 81)( 74, 80)( 75, 79)( 76, 78)( 82, 91)( 83, 93)( 84, 92)( 85, 99)( 86, 98)( 87, 97)( 88, 96)( 89, 95)( 90, 94)(100,108)(101,107)(102,106)(103,105)(109,118)(110,120)(111,119)(112,126)(113,125)(114,124)(115,123)(116,122)(117,121)(127,135)(128,134)(129,133)(130,132)(136,145)(137,147)(138,146)(139,153)(140,152)(141,151)(142,150)(143,149)(144,148)(154,162)(155,161)(156,160)(157,159)(163,172)(164,174)(165,173)(166,180)(167,179)(168,178)(169,177)(170,176)(171,175)(181,189)(182,188)(183,187)(184,186)(190,199)(191,201)(192,200)(193,207)(194,206)(195,205)(196,204)(197,203)(198,202)(208,216)(209,215)(210,214)(211,213);; 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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(216)!( 55, 82)( 56, 83)( 57, 84)( 58, 85)( 59, 86)( 60, 87)( 61, 88)( 62, 89)( 63, 90)( 64, 91)( 65, 92)( 66, 93)( 67, 94)( 68, 95)( 69, 96)( 70, 97)( 71, 98)( 72, 99)( 73,100)( 74,101)( 75,102)( 76,103)( 77,104)( 78,105)( 79,106)( 80,107)( 81,108)(109,163)(110,164)(111,165)(112,166)(113,167)(114,168)(115,169)(116,170)(117,171)(118,172)(119,173)(120,174)(121,175)(122,176)(123,177)(124,178)(125,179)(126,180)(127,181)(128,182)(129,183)(130,184)(131,185)(132,186)(133,187)(134,188)(135,189)(136,190)(137,191)(138,192)(139,193)(140,194)(141,195)(142,196)(143,197)(144,198)(145,199)(146,200)(147,201)(148,202)(149,203)(150,204)(151,205)(152,206)(153,207)(154,208)(155,209)(156,210)(157,211)(158,212)(159,213)(160,214)(161,215)(162,216); s1 := Sym(216)!( 1,109)( 2,111)( 3,110)( 4,117)( 5,116)( 6,115)( 7,114)( 8,113)( 9,112)( 10,135)( 11,134)( 12,133)( 13,132)( 14,131)( 15,130)( 16,129)( 17,128)( 18,127)( 19,126)( 20,125)( 21,124)( 22,123)( 23,122)( 24,121)( 25,120)( 26,119)( 27,118)( 28,136)( 29,138)( 30,137)( 31,144)( 32,143)( 33,142)( 34,141)( 35,140)( 36,139)( 37,162)( 38,161)( 39,160)( 40,159)( 41,158)( 42,157)( 43,156)( 44,155)( 45,154)( 46,153)( 47,152)( 48,151)( 49,150)( 50,149)( 51,148)( 52,147)( 53,146)( 54,145)( 55,190)( 56,192)( 57,191)( 58,198)( 59,197)( 60,196)( 61,195)( 62,194)( 63,193)( 64,216)( 65,215)( 66,214)( 67,213)( 68,212)( 69,211)( 70,210)( 71,209)( 72,208)( 73,207)( 74,206)( 75,205)( 76,204)( 77,203)( 78,202)( 79,201)( 80,200)( 81,199)( 82,163)( 83,165)( 84,164)( 85,171)( 86,170)( 87,169)( 88,168)( 89,167)( 90,166)( 91,189)( 92,188)( 93,187)( 94,186)( 95,185)( 96,184)( 97,183)( 98,182)( 99,181)(100,180)(101,179)(102,178)(103,177)(104,176)(105,175)(106,174)(107,173)(108,172); s2 := Sym(216)!( 1, 10)( 2, 12)( 3, 11)( 4, 18)( 5, 17)( 6, 16)( 7, 15)( 8, 14)( 9, 13)( 19, 27)( 20, 26)( 21, 25)( 22, 24)( 28, 37)( 29, 39)( 30, 38)( 31, 45)( 32, 44)( 33, 43)( 34, 42)( 35, 41)( 36, 40)( 46, 54)( 47, 53)( 48, 52)( 49, 51)( 55, 64)( 56, 66)( 57, 65)( 58, 72)( 59, 71)( 60, 70)( 61, 69)( 62, 68)( 63, 67)( 73, 81)( 74, 80)( 75, 79)( 76, 78)( 82, 91)( 83, 93)( 84, 92)( 85, 99)( 86, 98)( 87, 97)( 88, 96)( 89, 95)( 90, 94)(100,108)(101,107)(102,106)(103,105)(109,118)(110,120)(111,119)(112,126)(113,125)(114,124)(115,123)(116,122)(117,121)(127,135)(128,134)(129,133)(130,132)(136,145)(137,147)(138,146)(139,153)(140,152)(141,151)(142,150)(143,149)(144,148)(154,162)(155,161)(156,160)(157,159)(163,172)(164,174)(165,173)(166,180)(167,179)(168,178)(169,177)(170,176)(171,175)(181,189)(182,188)(183,187)(184,186)(190,199)(191,201)(192,200)(193,207)(194,206)(195,205)(196,204)(197,203)(198,202)(208,216)(209,215)(210,214)(211,213); poly := sub<Sym(216)|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 >;
References
None.
to this polytope.