Overview
- Group
- SmallGroup(1280,90280)
- Rank
- 3
- Schläfli Type
- {40,4}
- Vertices, edges, …
- 160, 320, 16
- 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)^2*(s2*s1*s0)^2*(s1*s2)^2, (s0*s1)^6*s0*s2*(s1*s0)^3*s1*s2> of order 4
6 facets
40 vertex figures
- 40 of {4}*8
Representations
Permutation Representation (GAP)
s0 := ( 1, 81)( 2, 85)( 3, 84)( 4, 83)( 5, 82)( 6, 86)( 7, 90)( 8, 89)( 9, 88)( 10, 87)( 11, 91)( 12, 95)( 13, 94)( 14, 93)( 15, 92)( 16, 96)( 17,100)( 18, 99)( 19, 98)( 20, 97)( 21,106)( 22,110)( 23,109)( 24,108)( 25,107)( 26,101)( 27,105)( 28,104)( 29,103)( 30,102)( 31,116)( 32,120)( 33,119)( 34,118)( 35,117)( 36,111)( 37,115)( 38,114)( 39,113)( 40,112)( 41,156)( 42,160)( 43,159)( 44,158)( 45,157)( 46,151)( 47,155)( 48,154)( 49,153)( 50,152)( 51,146)( 52,150)( 53,149)( 54,148)( 55,147)( 56,141)( 57,145)( 58,144)( 59,143)( 60,142)( 61,136)( 62,140)( 63,139)( 64,138)( 65,137)( 66,131)( 67,135)( 68,134)( 69,133)( 70,132)( 71,126)( 72,130)( 73,129)( 74,128)( 75,127)( 76,121)( 77,125)( 78,124)( 79,123)( 80,122);; 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 := ( 11, 16)( 12, 17)( 13, 18)( 14, 19)( 15, 20)( 31, 36)( 32, 37)( 33, 38)( 34, 39)( 35, 40)( 41, 76)( 42, 77)( 43, 78)( 44, 79)( 45, 80)( 46, 71)( 47, 72)( 48, 73)( 49, 74)( 50, 75)( 51, 61)( 52, 62)( 53, 63)( 54, 64)( 55, 65)( 56, 66)( 57, 67)( 58, 68)( 59, 69)( 60, 70)( 91, 96)( 92, 97)( 93, 98)( 94, 99)( 95,100)(111,116)(112,117)(113,118)(114,119)(115,120)(121,156)(122,157)(123,158)(124,159)(125,160)(126,151)(127,152)(128,153)(129,154)(130,155)(131,141)(132,142)(133,143)(134,144)(135,145)(136,146)(137,147)(138,148)(139,149)(140,150);; 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, s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*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)!( 1, 81)( 2, 85)( 3, 84)( 4, 83)( 5, 82)( 6, 86)( 7, 90)( 8, 89)( 9, 88)( 10, 87)( 11, 91)( 12, 95)( 13, 94)( 14, 93)( 15, 92)( 16, 96)( 17,100)( 18, 99)( 19, 98)( 20, 97)( 21,106)( 22,110)( 23,109)( 24,108)( 25,107)( 26,101)( 27,105)( 28,104)( 29,103)( 30,102)( 31,116)( 32,120)( 33,119)( 34,118)( 35,117)( 36,111)( 37,115)( 38,114)( 39,113)( 40,112)( 41,156)( 42,160)( 43,159)( 44,158)( 45,157)( 46,151)( 47,155)( 48,154)( 49,153)( 50,152)( 51,146)( 52,150)( 53,149)( 54,148)( 55,147)( 56,141)( 57,145)( 58,144)( 59,143)( 60,142)( 61,136)( 62,140)( 63,139)( 64,138)( 65,137)( 66,131)( 67,135)( 68,134)( 69,133)( 70,132)( 71,126)( 72,130)( 73,129)( 74,128)( 75,127)( 76,121)( 77,125)( 78,124)( 79,123)( 80,122); 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)!( 11, 16)( 12, 17)( 13, 18)( 14, 19)( 15, 20)( 31, 36)( 32, 37)( 33, 38)( 34, 39)( 35, 40)( 41, 76)( 42, 77)( 43, 78)( 44, 79)( 45, 80)( 46, 71)( 47, 72)( 48, 73)( 49, 74)( 50, 75)( 51, 61)( 52, 62)( 53, 63)( 54, 64)( 55, 65)( 56, 66)( 57, 67)( 58, 68)( 59, 69)( 60, 70)( 91, 96)( 92, 97)( 93, 98)( 94, 99)( 95,100)(111,116)(112,117)(113,118)(114,119)(115,120)(121,156)(122,157)(123,158)(124,159)(125,160)(126,151)(127,152)(128,153)(129,154)(130,155)(131,141)(132,142)(133,143)(134,144)(135,145)(136,146)(137,147)(138,148)(139,149)(140,150); 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, s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*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.