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