Overview
- Group
- SmallGroup(720,672)
- Rank
- 3
- Schläfli Type
- {30,12}
- Vertices, edges, …
- 30, 180, 12
- Order of s0s1s2
- 60
- Order of s0s1s2s1
- 2
- Also known as
- {30,12|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
12-fold
15-fold
18-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 := ( 2, 5)( 3, 4)( 6, 11)( 7, 15)( 8, 14)( 9, 13)( 10, 12)( 17, 20)( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 32, 35)( 33, 34)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 47, 50)( 48, 49)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 62, 65)( 63, 64)( 66, 71)( 67, 75)( 68, 74)( 69, 73)( 70, 72)( 77, 80)( 78, 79)( 81, 86)( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 92, 95)( 93, 94)( 96,101)( 97,105)( 98,104)( 99,103)(100,102)(107,110)(108,109)(111,116)(112,120)(113,119)(114,118)(115,117)(122,125)(123,124)(126,131)(127,135)(128,134)(129,133)(130,132)(137,140)(138,139)(141,146)(142,150)(143,149)(144,148)(145,147)(152,155)(153,154)(156,161)(157,165)(158,164)(159,163)(160,162)(167,170)(168,169)(171,176)(172,180)(173,179)(174,178)(175,177);; s1 := ( 1, 7)( 2, 6)( 3, 10)( 4, 9)( 5, 8)( 11, 12)( 13, 15)( 16, 37)( 17, 36)( 18, 40)( 19, 39)( 20, 38)( 21, 32)( 22, 31)( 23, 35)( 24, 34)( 25, 33)( 26, 42)( 27, 41)( 28, 45)( 29, 44)( 30, 43)( 46, 52)( 47, 51)( 48, 55)( 49, 54)( 50, 53)( 56, 57)( 58, 60)( 61, 82)( 62, 81)( 63, 85)( 64, 84)( 65, 83)( 66, 77)( 67, 76)( 68, 80)( 69, 79)( 70, 78)( 71, 87)( 72, 86)( 73, 90)( 74, 89)( 75, 88)( 91,142)( 92,141)( 93,145)( 94,144)( 95,143)( 96,137)( 97,136)( 98,140)( 99,139)(100,138)(101,147)(102,146)(103,150)(104,149)(105,148)(106,172)(107,171)(108,175)(109,174)(110,173)(111,167)(112,166)(113,170)(114,169)(115,168)(116,177)(117,176)(118,180)(119,179)(120,178)(121,157)(122,156)(123,160)(124,159)(125,158)(126,152)(127,151)(128,155)(129,154)(130,153)(131,162)(132,161)(133,165)(134,164)(135,163);; s2 := ( 1,106)( 2,107)( 3,108)( 4,109)( 5,110)( 6,111)( 7,112)( 8,113)( 9,114)( 10,115)( 11,116)( 12,117)( 13,118)( 14,119)( 15,120)( 16, 91)( 17, 92)( 18, 93)( 19, 94)( 20, 95)( 21, 96)( 22, 97)( 23, 98)( 24, 99)( 25,100)( 26,101)( 27,102)( 28,103)( 29,104)( 30,105)( 31,121)( 32,122)( 33,123)( 34,124)( 35,125)( 36,126)( 37,127)( 38,128)( 39,129)( 40,130)( 41,131)( 42,132)( 43,133)( 44,134)( 45,135)( 46,151)( 47,152)( 48,153)( 49,154)( 50,155)( 51,156)( 52,157)( 53,158)( 54,159)( 55,160)( 56,161)( 57,162)( 58,163)( 59,164)( 60,165)( 61,136)( 62,137)( 63,138)( 64,139)( 65,140)( 66,141)( 67,142)( 68,143)( 69,144)( 70,145)( 71,146)( 72,147)( 73,148)( 74,149)( 75,150)( 76,166)( 77,167)( 78,168)( 79,169)( 80,170)( 81,171)( 82,172)( 83,173)( 84,174)( 85,175)( 86,176)( 87,177)( 88,178)( 89,179)( 90,180);; 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*s1*s2*s1*s2*s1*s2*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(180)!( 2, 5)( 3, 4)( 6, 11)( 7, 15)( 8, 14)( 9, 13)( 10, 12)( 17, 20)( 18, 19)( 21, 26)( 22, 30)( 23, 29)( 24, 28)( 25, 27)( 32, 35)( 33, 34)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 47, 50)( 48, 49)( 51, 56)( 52, 60)( 53, 59)( 54, 58)( 55, 57)( 62, 65)( 63, 64)( 66, 71)( 67, 75)( 68, 74)( 69, 73)( 70, 72)( 77, 80)( 78, 79)( 81, 86)( 82, 90)( 83, 89)( 84, 88)( 85, 87)( 92, 95)( 93, 94)( 96,101)( 97,105)( 98,104)( 99,103)(100,102)(107,110)(108,109)(111,116)(112,120)(113,119)(114,118)(115,117)(122,125)(123,124)(126,131)(127,135)(128,134)(129,133)(130,132)(137,140)(138,139)(141,146)(142,150)(143,149)(144,148)(145,147)(152,155)(153,154)(156,161)(157,165)(158,164)(159,163)(160,162)(167,170)(168,169)(171,176)(172,180)(173,179)(174,178)(175,177); s1 := Sym(180)!( 1, 7)( 2, 6)( 3, 10)( 4, 9)( 5, 8)( 11, 12)( 13, 15)( 16, 37)( 17, 36)( 18, 40)( 19, 39)( 20, 38)( 21, 32)( 22, 31)( 23, 35)( 24, 34)( 25, 33)( 26, 42)( 27, 41)( 28, 45)( 29, 44)( 30, 43)( 46, 52)( 47, 51)( 48, 55)( 49, 54)( 50, 53)( 56, 57)( 58, 60)( 61, 82)( 62, 81)( 63, 85)( 64, 84)( 65, 83)( 66, 77)( 67, 76)( 68, 80)( 69, 79)( 70, 78)( 71, 87)( 72, 86)( 73, 90)( 74, 89)( 75, 88)( 91,142)( 92,141)( 93,145)( 94,144)( 95,143)( 96,137)( 97,136)( 98,140)( 99,139)(100,138)(101,147)(102,146)(103,150)(104,149)(105,148)(106,172)(107,171)(108,175)(109,174)(110,173)(111,167)(112,166)(113,170)(114,169)(115,168)(116,177)(117,176)(118,180)(119,179)(120,178)(121,157)(122,156)(123,160)(124,159)(125,158)(126,152)(127,151)(128,155)(129,154)(130,153)(131,162)(132,161)(133,165)(134,164)(135,163); s2 := Sym(180)!( 1,106)( 2,107)( 3,108)( 4,109)( 5,110)( 6,111)( 7,112)( 8,113)( 9,114)( 10,115)( 11,116)( 12,117)( 13,118)( 14,119)( 15,120)( 16, 91)( 17, 92)( 18, 93)( 19, 94)( 20, 95)( 21, 96)( 22, 97)( 23, 98)( 24, 99)( 25,100)( 26,101)( 27,102)( 28,103)( 29,104)( 30,105)( 31,121)( 32,122)( 33,123)( 34,124)( 35,125)( 36,126)( 37,127)( 38,128)( 39,129)( 40,130)( 41,131)( 42,132)( 43,133)( 44,134)( 45,135)( 46,151)( 47,152)( 48,153)( 49,154)( 50,155)( 51,156)( 52,157)( 53,158)( 54,159)( 55,160)( 56,161)( 57,162)( 58,163)( 59,164)( 60,165)( 61,136)( 62,137)( 63,138)( 64,139)( 65,140)( 66,141)( 67,142)( 68,143)( 69,144)( 70,145)( 71,146)( 72,147)( 73,148)( 74,149)( 75,150)( 76,166)( 77,167)( 78,168)( 79,169)( 80,170)( 81,171)( 82,172)( 83,173)( 84,174)( 85,175)( 86,176)( 87,177)( 88,178)( 89,179)( 90,180); 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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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 >;
References
None.
to this polytope.