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