Overview
- Group
- SmallGroup(864,98)
- Rank
- 3
- Schläfli Type
- {4,108}
- Vertices, edges, …
- 4, 216, 108
- Order of s0s1s2
- 108
- Order of s0s1s2s1
- 2
- Also known as
- {4,108|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 := (109,136)(110,137)(111,138)(112,139)(113,140)(114,141)(115,142)(116,143)(117,144)(118,145)(119,146)(120,147)(121,148)(122,149)(123,150)(124,151)(125,152)(126,153)(127,154)(128,155)(129,156)(130,157)(131,158)(132,159)(133,160)(134,161)(135,162)(163,190)(164,191)(165,192)(166,193)(167,194)(168,195)(169,196)(170,197)(171,198)(172,199)(173,200)(174,201)(175,202)(176,203)(177,204)(178,205)(179,206)(180,207)(181,208)(182,209)(183,210)(184,211)(185,212)(186,213)(187,214)(188,215)(189,216);; 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)( 55,163)( 56,165)( 57,164)( 58,171)( 59,170)( 60,169)( 61,168)( 62,167)( 63,166)( 64,189)( 65,188)( 66,187)( 67,186)( 68,185)( 69,184)( 70,183)( 71,182)( 72,181)( 73,180)( 74,179)( 75,178)( 76,177)( 77,176)( 78,175)( 79,174)( 80,173)( 81,172)( 82,190)( 83,192)( 84,191)( 85,198)( 86,197)( 87,196)( 88,195)( 89,194)( 90,193)( 91,216)( 92,215)( 93,214)( 94,213)( 95,212)( 96,211)( 97,210)( 98,209)( 99,208)(100,207)(101,206)(102,205)(103,204)(104,203)(105,202)(106,201)(107,200)(108,199);; 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)(109,172)(110,174)(111,173)(112,180)(113,179)(114,178)(115,177)(116,176)(117,175)(118,163)(119,165)(120,164)(121,171)(122,170)(123,169)(124,168)(125,167)(126,166)(127,189)(128,188)(129,187)(130,186)(131,185)(132,184)(133,183)(134,182)(135,181)(136,199)(137,201)(138,200)(139,207)(140,206)(141,205)(142,204)(143,203)(144,202)(145,190)(146,192)(147,191)(148,198)(149,197)(150,196)(151,195)(152,194)(153,193)(154,216)(155,215)(156,214)(157,213)(158,212)(159,211)(160,210)(161,209)(162,208);; 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*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*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*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)!(109,136)(110,137)(111,138)(112,139)(113,140)(114,141)(115,142)(116,143)(117,144)(118,145)(119,146)(120,147)(121,148)(122,149)(123,150)(124,151)(125,152)(126,153)(127,154)(128,155)(129,156)(130,157)(131,158)(132,159)(133,160)(134,161)(135,162)(163,190)(164,191)(165,192)(166,193)(167,194)(168,195)(169,196)(170,197)(171,198)(172,199)(173,200)(174,201)(175,202)(176,203)(177,204)(178,205)(179,206)(180,207)(181,208)(182,209)(183,210)(184,211)(185,212)(186,213)(187,214)(188,215)(189,216); 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)( 55,163)( 56,165)( 57,164)( 58,171)( 59,170)( 60,169)( 61,168)( 62,167)( 63,166)( 64,189)( 65,188)( 66,187)( 67,186)( 68,185)( 69,184)( 70,183)( 71,182)( 72,181)( 73,180)( 74,179)( 75,178)( 76,177)( 77,176)( 78,175)( 79,174)( 80,173)( 81,172)( 82,190)( 83,192)( 84,191)( 85,198)( 86,197)( 87,196)( 88,195)( 89,194)( 90,193)( 91,216)( 92,215)( 93,214)( 94,213)( 95,212)( 96,211)( 97,210)( 98,209)( 99,208)(100,207)(101,206)(102,205)(103,204)(104,203)(105,202)(106,201)(107,200)(108,199); 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)(109,172)(110,174)(111,173)(112,180)(113,179)(114,178)(115,177)(116,176)(117,175)(118,163)(119,165)(120,164)(121,171)(122,170)(123,169)(124,168)(125,167)(126,166)(127,189)(128,188)(129,187)(130,186)(131,185)(132,184)(133,183)(134,182)(135,181)(136,199)(137,201)(138,200)(139,207)(140,206)(141,205)(142,204)(143,203)(144,202)(145,190)(146,192)(147,191)(148,198)(149,197)(150,196)(151,195)(152,194)(153,193)(154,216)(155,215)(156,214)(157,213)(158,212)(159,211)(160,210)(161,209)(162,208); 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*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*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*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.