Overview
- Group
- SmallGroup(720,136)
- Rank
- 3
- Schläfli Type
- {10,36}
- Vertices, edges, …
- 10, 180, 36
- Order of s0s1s2
- 180
- Order of s0s1s2s1
- 2
- Also known as
- {10,36|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
5-fold
6-fold
9-fold
10-fold
15-fold
18-fold
20-fold
30-fold
36-fold
45-fold
60-fold
90-fold
Covers minimal covers in bold
2-fold
Irregular Quotients of which this is a minimal cover
None.
Representations
Permutation Representation (GAP)
s0 := ( 4, 13)( 5, 14)( 6, 15)( 7, 10)( 8, 11)( 9, 12)( 19, 28)( 20, 29)( 21, 30)( 22, 25)( 23, 26)( 24, 27)( 34, 43)( 35, 44)( 36, 45)( 37, 40)( 38, 41)( 39, 42)( 49, 58)( 50, 59)( 51, 60)( 52, 55)( 53, 56)( 54, 57)( 64, 73)( 65, 74)( 66, 75)( 67, 70)( 68, 71)( 69, 72)( 79, 88)( 80, 89)( 81, 90)( 82, 85)( 83, 86)( 84, 87)( 94,103)( 95,104)( 96,105)( 97,100)( 98,101)( 99,102)(109,118)(110,119)(111,120)(112,115)(113,116)(114,117)(124,133)(125,134)(126,135)(127,130)(128,131)(129,132)(139,148)(140,149)(141,150)(142,145)(143,146)(144,147)(154,163)(155,164)(156,165)(157,160)(158,161)(159,162)(169,178)(170,179)(171,180)(172,175)(173,176)(174,177);; s1 := ( 1, 4)( 2, 6)( 3, 5)( 7, 13)( 8, 15)( 9, 14)( 11, 12)( 16, 36)( 17, 35)( 18, 34)( 19, 33)( 20, 32)( 21, 31)( 22, 45)( 23, 44)( 24, 43)( 25, 42)( 26, 41)( 27, 40)( 28, 39)( 29, 38)( 30, 37)( 46, 49)( 47, 51)( 48, 50)( 52, 58)( 53, 60)( 54, 59)( 56, 57)( 61, 81)( 62, 80)( 63, 79)( 64, 78)( 65, 77)( 66, 76)( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71, 86)( 72, 85)( 73, 84)( 74, 83)( 75, 82)( 91,139)( 92,141)( 93,140)( 94,136)( 95,138)( 96,137)( 97,148)( 98,150)( 99,149)(100,145)(101,147)(102,146)(103,142)(104,144)(105,143)(106,171)(107,170)(108,169)(109,168)(110,167)(111,166)(112,180)(113,179)(114,178)(115,177)(116,176)(117,175)(118,174)(119,173)(120,172)(121,156)(122,155)(123,154)(124,153)(125,152)(126,151)(127,165)(128,164)(129,163)(130,162)(131,161)(132,160)(133,159)(134,158)(135,157);; s2 := ( 1,106)( 2,108)( 3,107)( 4,109)( 5,111)( 6,110)( 7,112)( 8,114)( 9,113)( 10,115)( 11,117)( 12,116)( 13,118)( 14,120)( 15,119)( 16, 91)( 17, 93)( 18, 92)( 19, 94)( 20, 96)( 21, 95)( 22, 97)( 23, 99)( 24, 98)( 25,100)( 26,102)( 27,101)( 28,103)( 29,105)( 30,104)( 31,123)( 32,122)( 33,121)( 34,126)( 35,125)( 36,124)( 37,129)( 38,128)( 39,127)( 40,132)( 41,131)( 42,130)( 43,135)( 44,134)( 45,133)( 46,151)( 47,153)( 48,152)( 49,154)( 50,156)( 51,155)( 52,157)( 53,159)( 54,158)( 55,160)( 56,162)( 57,161)( 58,163)( 59,165)( 60,164)( 61,136)( 62,138)( 63,137)( 64,139)( 65,141)( 66,140)( 67,142)( 68,144)( 69,143)( 70,145)( 71,147)( 72,146)( 73,148)( 74,150)( 75,149)( 76,168)( 77,167)( 78,166)( 79,171)( 80,170)( 81,169)( 82,174)( 83,173)( 84,172)( 85,177)( 86,176)( 87,175)( 88,180)( 89,179)( 90,178);; 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*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(180)!( 4, 13)( 5, 14)( 6, 15)( 7, 10)( 8, 11)( 9, 12)( 19, 28)( 20, 29)( 21, 30)( 22, 25)( 23, 26)( 24, 27)( 34, 43)( 35, 44)( 36, 45)( 37, 40)( 38, 41)( 39, 42)( 49, 58)( 50, 59)( 51, 60)( 52, 55)( 53, 56)( 54, 57)( 64, 73)( 65, 74)( 66, 75)( 67, 70)( 68, 71)( 69, 72)( 79, 88)( 80, 89)( 81, 90)( 82, 85)( 83, 86)( 84, 87)( 94,103)( 95,104)( 96,105)( 97,100)( 98,101)( 99,102)(109,118)(110,119)(111,120)(112,115)(113,116)(114,117)(124,133)(125,134)(126,135)(127,130)(128,131)(129,132)(139,148)(140,149)(141,150)(142,145)(143,146)(144,147)(154,163)(155,164)(156,165)(157,160)(158,161)(159,162)(169,178)(170,179)(171,180)(172,175)(173,176)(174,177); s1 := Sym(180)!( 1, 4)( 2, 6)( 3, 5)( 7, 13)( 8, 15)( 9, 14)( 11, 12)( 16, 36)( 17, 35)( 18, 34)( 19, 33)( 20, 32)( 21, 31)( 22, 45)( 23, 44)( 24, 43)( 25, 42)( 26, 41)( 27, 40)( 28, 39)( 29, 38)( 30, 37)( 46, 49)( 47, 51)( 48, 50)( 52, 58)( 53, 60)( 54, 59)( 56, 57)( 61, 81)( 62, 80)( 63, 79)( 64, 78)( 65, 77)( 66, 76)( 67, 90)( 68, 89)( 69, 88)( 70, 87)( 71, 86)( 72, 85)( 73, 84)( 74, 83)( 75, 82)( 91,139)( 92,141)( 93,140)( 94,136)( 95,138)( 96,137)( 97,148)( 98,150)( 99,149)(100,145)(101,147)(102,146)(103,142)(104,144)(105,143)(106,171)(107,170)(108,169)(109,168)(110,167)(111,166)(112,180)(113,179)(114,178)(115,177)(116,176)(117,175)(118,174)(119,173)(120,172)(121,156)(122,155)(123,154)(124,153)(125,152)(126,151)(127,165)(128,164)(129,163)(130,162)(131,161)(132,160)(133,159)(134,158)(135,157); s2 := Sym(180)!( 1,106)( 2,108)( 3,107)( 4,109)( 5,111)( 6,110)( 7,112)( 8,114)( 9,113)( 10,115)( 11,117)( 12,116)( 13,118)( 14,120)( 15,119)( 16, 91)( 17, 93)( 18, 92)( 19, 94)( 20, 96)( 21, 95)( 22, 97)( 23, 99)( 24, 98)( 25,100)( 26,102)( 27,101)( 28,103)( 29,105)( 30,104)( 31,123)( 32,122)( 33,121)( 34,126)( 35,125)( 36,124)( 37,129)( 38,128)( 39,127)( 40,132)( 41,131)( 42,130)( 43,135)( 44,134)( 45,133)( 46,151)( 47,153)( 48,152)( 49,154)( 50,156)( 51,155)( 52,157)( 53,159)( 54,158)( 55,160)( 56,162)( 57,161)( 58,163)( 59,165)( 60,164)( 61,136)( 62,138)( 63,137)( 64,139)( 65,141)( 66,140)( 67,142)( 68,144)( 69,143)( 70,145)( 71,147)( 72,146)( 73,148)( 74,150)( 75,149)( 76,168)( 77,167)( 78,166)( 79,171)( 80,170)( 81,169)( 82,174)( 83,173)( 84,172)( 85,177)( 86,176)( 87,175)( 88,180)( 89,179)( 90,178); poly := sub<Sym(180)|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*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 >;
References
None.
to this polytope.