Overview
- Group
- SmallGroup(1280,90280)
- Rank
- 3
- Schläfli Type
- {4,40}
- Vertices, edges, …
- 16, 320, 160
- 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*s2)^3*s1*s0*(s2*s1)^6*s2> of order 4
40 facets
- 40 of {4}*8
6 vertex figures
Representations
Permutation Representation (GAP)
s0 := ( 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);; 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, 83)( 2, 82)( 3, 81)( 4, 85)( 5, 84)( 6, 88)( 7, 87)( 8, 86)( 9, 90)( 10, 89)( 11, 93)( 12, 92)( 13, 91)( 14, 95)( 15, 94)( 16, 98)( 17, 97)( 18, 96)( 19,100)( 20, 99)( 21,108)( 22,107)( 23,106)( 24,110)( 25,109)( 26,103)( 27,102)( 28,101)( 29,105)( 30,104)( 31,118)( 32,117)( 33,116)( 34,120)( 35,119)( 36,113)( 37,112)( 38,111)( 39,115)( 40,114)( 41,158)( 42,157)( 43,156)( 44,160)( 45,159)( 46,153)( 47,152)( 48,151)( 49,155)( 50,154)( 51,148)( 52,147)( 53,146)( 54,150)( 55,149)( 56,143)( 57,142)( 58,141)( 59,145)( 60,144)( 61,138)( 62,137)( 63,136)( 64,140)( 65,139)( 66,133)( 67,132)( 68,131)( 69,135)( 70,134)( 71,128)( 72,127)( 73,126)( 74,130)( 75,129)( 76,123)( 77,122)( 78,121)( 79,125)( 80,124);; 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*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s0,
s1*s2*s1*s2*s0*s1*s0*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*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := 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); 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, 83)( 2, 82)( 3, 81)( 4, 85)( 5, 84)( 6, 88)( 7, 87)( 8, 86)( 9, 90)( 10, 89)( 11, 93)( 12, 92)( 13, 91)( 14, 95)( 15, 94)( 16, 98)( 17, 97)( 18, 96)( 19,100)( 20, 99)( 21,108)( 22,107)( 23,106)( 24,110)( 25,109)( 26,103)( 27,102)( 28,101)( 29,105)( 30,104)( 31,118)( 32,117)( 33,116)( 34,120)( 35,119)( 36,113)( 37,112)( 38,111)( 39,115)( 40,114)( 41,158)( 42,157)( 43,156)( 44,160)( 45,159)( 46,153)( 47,152)( 48,151)( 49,155)( 50,154)( 51,148)( 52,147)( 53,146)( 54,150)( 55,149)( 56,143)( 57,142)( 58,141)( 59,145)( 60,144)( 61,138)( 62,137)( 63,136)( 64,140)( 65,139)( 66,133)( 67,132)( 68,131)( 69,135)( 70,134)( 71,128)( 72,127)( 73,126)( 74,130)( 75,129)( 76,123)( 77,122)( 78,121)( 79,125)( 80,124); 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*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1, s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s0, s1*s2*s1*s2*s0*s1*s0*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*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2 >;
References
None.
to this polytope.