Overview
- Group
- SmallGroup(880,200)
- Rank
- 3
- Schläfli Type
- {4,110}
- Vertices, edges, …
- 4, 220, 110
- Order of s0s1s2
- 220
- Order of s0s1s2s1
- 2
- Also known as
- {4,110|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
5-fold
10-fold
11-fold
20-fold
22-fold
44-fold
55-fold
110-fold
Covers minimal covers in bold
2-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := (111,166)(112,167)(113,168)(114,169)(115,170)(116,171)(117,172)(118,173)(119,174)(120,175)(121,176)(122,177)(123,178)(124,179)(125,180)(126,181)(127,182)(128,183)(129,184)(130,185)(131,186)(132,187)(133,188)(134,189)(135,190)(136,191)(137,192)(138,193)(139,194)(140,195)(141,196)(142,197)(143,198)(144,199)(145,200)(146,201)(147,202)(148,203)(149,204)(150,205)(151,206)(152,207)(153,208)(154,209)(155,210)(156,211)(157,212)(158,213)(159,214)(160,215)(161,216)(162,217)(163,218)(164,219)(165,220);; s1 := ( 1,111)( 2,121)( 3,120)( 4,119)( 5,118)( 6,117)( 7,116)( 8,115)( 9,114)( 10,113)( 11,112)( 12,155)( 13,165)( 14,164)( 15,163)( 16,162)( 17,161)( 18,160)( 19,159)( 20,158)( 21,157)( 22,156)( 23,144)( 24,154)( 25,153)( 26,152)( 27,151)( 28,150)( 29,149)( 30,148)( 31,147)( 32,146)( 33,145)( 34,133)( 35,143)( 36,142)( 37,141)( 38,140)( 39,139)( 40,138)( 41,137)( 42,136)( 43,135)( 44,134)( 45,122)( 46,132)( 47,131)( 48,130)( 49,129)( 50,128)( 51,127)( 52,126)( 53,125)( 54,124)( 55,123)( 56,166)( 57,176)( 58,175)( 59,174)( 60,173)( 61,172)( 62,171)( 63,170)( 64,169)( 65,168)( 66,167)( 67,210)( 68,220)( 69,219)( 70,218)( 71,217)( 72,216)( 73,215)( 74,214)( 75,213)( 76,212)( 77,211)( 78,199)( 79,209)( 80,208)( 81,207)( 82,206)( 83,205)( 84,204)( 85,203)( 86,202)( 87,201)( 88,200)( 89,188)( 90,198)( 91,197)( 92,196)( 93,195)( 94,194)( 95,193)( 96,192)( 97,191)( 98,190)( 99,189)(100,177)(101,187)(102,186)(103,185)(104,184)(105,183)(106,182)(107,181)(108,180)(109,179)(110,178);; s2 := ( 1, 13)( 2, 12)( 3, 22)( 4, 21)( 5, 20)( 6, 19)( 7, 18)( 8, 17)( 9, 16)( 10, 15)( 11, 14)( 23, 46)( 24, 45)( 25, 55)( 26, 54)( 27, 53)( 28, 52)( 29, 51)( 30, 50)( 31, 49)( 32, 48)( 33, 47)( 34, 35)( 36, 44)( 37, 43)( 38, 42)( 39, 41)( 56, 68)( 57, 67)( 58, 77)( 59, 76)( 60, 75)( 61, 74)( 62, 73)( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 78,101)( 79,100)( 80,110)( 81,109)( 82,108)( 83,107)( 84,106)( 85,105)( 86,104)( 87,103)( 88,102)( 89, 90)( 91, 99)( 92, 98)( 93, 97)( 94, 96)(111,123)(112,122)(113,132)(114,131)(115,130)(116,129)(117,128)(118,127)(119,126)(120,125)(121,124)(133,156)(134,155)(135,165)(136,164)(137,163)(138,162)(139,161)(140,160)(141,159)(142,158)(143,157)(144,145)(146,154)(147,153)(148,152)(149,151)(166,178)(167,177)(168,187)(169,186)(170,185)(171,184)(172,183)(173,182)(174,181)(175,180)(176,179)(188,211)(189,210)(190,220)(191,219)(192,218)(193,217)(194,216)(195,215)(196,214)(197,213)(198,212)(199,200)(201,209)(202,208)(203,207)(204,206);; 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*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(220)!(111,166)(112,167)(113,168)(114,169)(115,170)(116,171)(117,172)(118,173)(119,174)(120,175)(121,176)(122,177)(123,178)(124,179)(125,180)(126,181)(127,182)(128,183)(129,184)(130,185)(131,186)(132,187)(133,188)(134,189)(135,190)(136,191)(137,192)(138,193)(139,194)(140,195)(141,196)(142,197)(143,198)(144,199)(145,200)(146,201)(147,202)(148,203)(149,204)(150,205)(151,206)(152,207)(153,208)(154,209)(155,210)(156,211)(157,212)(158,213)(159,214)(160,215)(161,216)(162,217)(163,218)(164,219)(165,220); s1 := Sym(220)!( 1,111)( 2,121)( 3,120)( 4,119)( 5,118)( 6,117)( 7,116)( 8,115)( 9,114)( 10,113)( 11,112)( 12,155)( 13,165)( 14,164)( 15,163)( 16,162)( 17,161)( 18,160)( 19,159)( 20,158)( 21,157)( 22,156)( 23,144)( 24,154)( 25,153)( 26,152)( 27,151)( 28,150)( 29,149)( 30,148)( 31,147)( 32,146)( 33,145)( 34,133)( 35,143)( 36,142)( 37,141)( 38,140)( 39,139)( 40,138)( 41,137)( 42,136)( 43,135)( 44,134)( 45,122)( 46,132)( 47,131)( 48,130)( 49,129)( 50,128)( 51,127)( 52,126)( 53,125)( 54,124)( 55,123)( 56,166)( 57,176)( 58,175)( 59,174)( 60,173)( 61,172)( 62,171)( 63,170)( 64,169)( 65,168)( 66,167)( 67,210)( 68,220)( 69,219)( 70,218)( 71,217)( 72,216)( 73,215)( 74,214)( 75,213)( 76,212)( 77,211)( 78,199)( 79,209)( 80,208)( 81,207)( 82,206)( 83,205)( 84,204)( 85,203)( 86,202)( 87,201)( 88,200)( 89,188)( 90,198)( 91,197)( 92,196)( 93,195)( 94,194)( 95,193)( 96,192)( 97,191)( 98,190)( 99,189)(100,177)(101,187)(102,186)(103,185)(104,184)(105,183)(106,182)(107,181)(108,180)(109,179)(110,178); s2 := Sym(220)!( 1, 13)( 2, 12)( 3, 22)( 4, 21)( 5, 20)( 6, 19)( 7, 18)( 8, 17)( 9, 16)( 10, 15)( 11, 14)( 23, 46)( 24, 45)( 25, 55)( 26, 54)( 27, 53)( 28, 52)( 29, 51)( 30, 50)( 31, 49)( 32, 48)( 33, 47)( 34, 35)( 36, 44)( 37, 43)( 38, 42)( 39, 41)( 56, 68)( 57, 67)( 58, 77)( 59, 76)( 60, 75)( 61, 74)( 62, 73)( 63, 72)( 64, 71)( 65, 70)( 66, 69)( 78,101)( 79,100)( 80,110)( 81,109)( 82,108)( 83,107)( 84,106)( 85,105)( 86,104)( 87,103)( 88,102)( 89, 90)( 91, 99)( 92, 98)( 93, 97)( 94, 96)(111,123)(112,122)(113,132)(114,131)(115,130)(116,129)(117,128)(118,127)(119,126)(120,125)(121,124)(133,156)(134,155)(135,165)(136,164)(137,163)(138,162)(139,161)(140,160)(141,159)(142,158)(143,157)(144,145)(146,154)(147,153)(148,152)(149,151)(166,178)(167,177)(168,187)(169,186)(170,185)(171,184)(172,183)(173,182)(174,181)(175,180)(176,179)(188,211)(189,210)(190,220)(191,219)(192,218)(193,217)(194,216)(195,215)(196,214)(197,213)(198,212)(199,200)(201,209)(202,208)(203,207)(204,206); poly := sub<Sym(220)|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*s1*s2*s1*s2 >;
References
None.
to this polytope.