Overview
- Group
- SmallGroup(1280,90281)
- Rank
- 3
- Schläfli Type
- {8,20}
- Vertices, edges, …
- 32, 320, 80
- Order of s0s1s2
- 20
- Order of s0s1s2s1
- 8
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Orientable
Quotients maximal quotients in bold
2-fold
4-fold
5-fold
8-fold
10-fold
16-fold
20-fold
32-fold
40-fold
64-fold
80-fold
160-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
P/N, where N=<(s0*s1)^4, s0*s1*s2*(s1*s0)^3*s1*s2*s1> of order 4
30 facets
8 vertex figures
- 8 of {20}*40
Representations
Permutation Representation (GAP)
s0 := ( 1, 81)( 2, 82)( 3, 83)( 4, 84)( 5, 85)( 6, 86)( 7, 87)( 8, 88)( 9, 89)( 10, 90)( 11, 91)( 12, 92)( 13, 93)( 14, 94)( 15, 95)( 16, 96)( 17, 97)( 18, 98)( 19, 99)( 20,100)( 21,106)( 22,107)( 23,108)( 24,109)( 25,110)( 26,101)( 27,102)( 28,103)( 29,104)( 30,105)( 31,116)( 32,117)( 33,118)( 34,119)( 35,120)( 36,111)( 37,112)( 38,113)( 39,114)( 40,115)( 41,156)( 42,157)( 43,158)( 44,159)( 45,160)( 46,151)( 47,152)( 48,153)( 49,154)( 50,155)( 51,146)( 52,147)( 53,148)( 54,149)( 55,150)( 56,141)( 57,142)( 58,143)( 59,144)( 60,145)( 61,136)( 62,137)( 63,138)( 64,139)( 65,140)( 66,131)( 67,132)( 68,133)( 69,134)( 70,135)( 71,126)( 72,127)( 73,128)( 74,129)( 75,130)( 76,121)( 77,122)( 78,123)( 79,124)( 80,125);; s1 := ( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)( 21, 31)( 22, 35)( 23, 34)( 24, 33)( 25, 32)( 26, 36)( 27, 40)( 28, 39)( 29, 38)( 30, 37)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)( 58, 59)( 61, 71)( 62, 75)( 63, 74)( 64, 73)( 65, 72)( 66, 76)( 67, 80)( 68, 79)( 69, 78)( 70, 77)( 81,121)( 82,125)( 83,124)( 84,123)( 85,122)( 86,126)( 87,130)( 88,129)( 89,128)( 90,127)( 91,131)( 92,135)( 93,134)( 94,133)( 95,132)( 96,136)( 97,140)( 98,139)( 99,138)(100,137)(101,151)(102,155)(103,154)(104,153)(105,152)(106,156)(107,160)(108,159)(109,158)(110,157)(111,141)(112,145)(113,144)(114,143)(115,142)(116,146)(117,150)(118,149)(119,148)(120,147);; s2 := ( 1, 3)( 4, 5)( 6, 8)( 9, 10)( 11, 18)( 12, 17)( 13, 16)( 14, 20)( 15, 19)( 21, 23)( 24, 25)( 26, 28)( 29, 30)( 31, 38)( 32, 37)( 33, 36)( 34, 40)( 35, 39)( 41, 78)( 42, 77)( 43, 76)( 44, 80)( 45, 79)( 46, 73)( 47, 72)( 48, 71)( 49, 75)( 50, 74)( 51, 63)( 52, 62)( 53, 61)( 54, 65)( 55, 64)( 56, 68)( 57, 67)( 58, 66)( 59, 70)( 60, 69)( 81, 83)( 84, 85)( 86, 88)( 89, 90)( 91, 98)( 92, 97)( 93, 96)( 94,100)( 95, 99)(101,103)(104,105)(106,108)(109,110)(111,118)(112,117)(113,116)(114,120)(115,119)(121,158)(122,157)(123,156)(124,160)(125,159)(126,153)(127,152)(128,151)(129,155)(130,154)(131,143)(132,142)(133,141)(134,145)(135,144)(136,148)(137,147)(138,146)(139,150)(140,149);; 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*s2*s1*s0*s1*s0*s2*s1*s0*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(160)!( 1, 81)( 2, 82)( 3, 83)( 4, 84)( 5, 85)( 6, 86)( 7, 87)( 8, 88)( 9, 89)( 10, 90)( 11, 91)( 12, 92)( 13, 93)( 14, 94)( 15, 95)( 16, 96)( 17, 97)( 18, 98)( 19, 99)( 20,100)( 21,106)( 22,107)( 23,108)( 24,109)( 25,110)( 26,101)( 27,102)( 28,103)( 29,104)( 30,105)( 31,116)( 32,117)( 33,118)( 34,119)( 35,120)( 36,111)( 37,112)( 38,113)( 39,114)( 40,115)( 41,156)( 42,157)( 43,158)( 44,159)( 45,160)( 46,151)( 47,152)( 48,153)( 49,154)( 50,155)( 51,146)( 52,147)( 53,148)( 54,149)( 55,150)( 56,141)( 57,142)( 58,143)( 59,144)( 60,145)( 61,136)( 62,137)( 63,138)( 64,139)( 65,140)( 66,131)( 67,132)( 68,133)( 69,134)( 70,135)( 71,126)( 72,127)( 73,128)( 74,129)( 75,130)( 76,121)( 77,122)( 78,123)( 79,124)( 80,125); s1 := Sym(160)!( 2, 5)( 3, 4)( 7, 10)( 8, 9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)( 21, 31)( 22, 35)( 23, 34)( 24, 33)( 25, 32)( 26, 36)( 27, 40)( 28, 39)( 29, 38)( 30, 37)( 42, 45)( 43, 44)( 47, 50)( 48, 49)( 52, 55)( 53, 54)( 57, 60)( 58, 59)( 61, 71)( 62, 75)( 63, 74)( 64, 73)( 65, 72)( 66, 76)( 67, 80)( 68, 79)( 69, 78)( 70, 77)( 81,121)( 82,125)( 83,124)( 84,123)( 85,122)( 86,126)( 87,130)( 88,129)( 89,128)( 90,127)( 91,131)( 92,135)( 93,134)( 94,133)( 95,132)( 96,136)( 97,140)( 98,139)( 99,138)(100,137)(101,151)(102,155)(103,154)(104,153)(105,152)(106,156)(107,160)(108,159)(109,158)(110,157)(111,141)(112,145)(113,144)(114,143)(115,142)(116,146)(117,150)(118,149)(119,148)(120,147); s2 := Sym(160)!( 1, 3)( 4, 5)( 6, 8)( 9, 10)( 11, 18)( 12, 17)( 13, 16)( 14, 20)( 15, 19)( 21, 23)( 24, 25)( 26, 28)( 29, 30)( 31, 38)( 32, 37)( 33, 36)( 34, 40)( 35, 39)( 41, 78)( 42, 77)( 43, 76)( 44, 80)( 45, 79)( 46, 73)( 47, 72)( 48, 71)( 49, 75)( 50, 74)( 51, 63)( 52, 62)( 53, 61)( 54, 65)( 55, 64)( 56, 68)( 57, 67)( 58, 66)( 59, 70)( 60, 69)( 81, 83)( 84, 85)( 86, 88)( 89, 90)( 91, 98)( 92, 97)( 93, 96)( 94,100)( 95, 99)(101,103)(104,105)(106,108)(109,110)(111,118)(112,117)(113,116)(114,120)(115,119)(121,158)(122,157)(123,156)(124,160)(125,159)(126,153)(127,152)(128,151)(129,155)(130,154)(131,143)(132,142)(133,141)(134,145)(135,144)(136,148)(137,147)(138,146)(139,150)(140,149); poly := sub<Sym(160)|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*s2*s1*s0*s1*s0*s2*s1*s0*s2*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 >;
References
None.
to this polytope.