Overview
- Group
- SmallGroup(1280,1116459)
- Rank
- 3
- Schläfli Type
- {8,10}
- Vertices, edges, …
- 64, 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
8-fold
32-fold
64-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*(s2*s1)^2*s0*s2*s1*s0*(s2*s1)^2> of order 2
40 facets
- 40 of {8}*16
32 vertex figures
- 32 of {10}*20
P/N, where N=<s0*s1*s0*s2*s1*s0*(s2*s1)^2*s0*s2*s1*s2> of order 2
40 facets
- 40 of {8}*16
32 vertex figures
- 32 of {10}*20
P/N, where N=<s0*s1*s2*(s1*s0)^2*(s2*s1)^2*s0*s1*s2> of order 2
40 facets
- 40 of {8}*16
32 vertex figures
- 32 of {10}*20
P/N, where N=<(s0*s1)^2*s2*s1*s0*(s2*s1)^2*s0*s1*s0*(s2*s1)^2*s2> of order 2
40 facets
- 40 of {8}*16
32 vertex figures
- 32 of {10}*20
P/N, where N=<s1*s0*(s1*s2)^2*s1*s0*s2*s1*s0*(s2*s1)^2> of order 2
40 facets
- 40 of {8}*16
32 vertex figures
- 32 of {10}*20
P/N, where N=<s0*(s2*s1)^2*s0*s2*s1*s0*(s2*s1)^2, s1*s0*(s2*s1)^2*(s0*s2*s1)^2*s2> of order 4
20 facets
- 20 of {8}*16
16 vertex figures
- 16 of {10}*20
P/N, where N=<s0*s1*(s0*(s2*s1)^2)^2*s2, s1*(s2*s1*s0)^3*s2*s1*s2> of order 4
20 facets
- 20 of {8}*16
16 vertex figures
- 16 of {10}*20
P/N, where N=<s0*s1*s2*(s1*s0)^2*(s2*s1)^2*s0*s1*s2, s0*s1*(s2*s1*s0)^2*(s2*s1)^3> of order 4
20 facets
- 20 of {8}*16
16 vertex figures
- 16 of {10}*20
Representations
Permutation Representation (GAP)
s0 := ( 1,101)( 2,102)( 3,104)( 4,103)( 5, 97)( 6, 98)( 7,100)( 8, 99)( 9,110)( 10,109)( 11,111)( 12,112)( 13,106)( 14,105)( 15,107)( 16,108)( 17,117)( 18,118)( 19,120)( 20,119)( 21,113)( 22,114)( 23,116)( 24,115)( 25,126)( 26,125)( 27,127)( 28,128)( 29,122)( 30,121)( 31,123)( 32,124)( 33, 69)( 34, 70)( 35, 72)( 36, 71)( 37, 65)( 38, 66)( 39, 68)( 40, 67)( 41, 78)( 42, 77)( 43, 79)( 44, 80)( 45, 74)( 46, 73)( 47, 75)( 48, 76)( 49, 85)( 50, 86)( 51, 88)( 52, 87)( 53, 81)( 54, 82)( 55, 84)( 56, 83)( 57, 94)( 58, 93)( 59, 95)( 60, 96)( 61, 90)( 62, 89)( 63, 91)( 64, 92);; s1 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)( 14, 16)( 17, 28)( 18, 27)( 19, 26)( 20, 25)( 21, 32)( 22, 31)( 23, 30)( 24, 29)( 33, 43)( 34, 44)( 35, 41)( 36, 42)( 37, 47)( 38, 48)( 39, 45)( 40, 46)( 49, 52)( 50, 51)( 53, 56)( 54, 55)( 57, 60)( 58, 59)( 61, 64)( 62, 63)( 65,123)( 66,124)( 67,121)( 68,122)( 69,127)( 70,128)( 71,125)( 72,126)( 73,115)( 74,116)( 75,113)( 76,114)( 77,119)( 78,120)( 79,117)( 80,118)( 81, 99)( 82,100)( 83, 97)( 84, 98)( 85,103)( 86,104)( 87,101)( 88,102)( 89,107)( 90,108)( 91,105)( 92,106)( 93,111)( 94,112)( 95,109)( 96,110);; s2 := ( 9,121)( 10,122)( 11,123)( 12,124)( 13,125)( 14,126)( 15,127)( 16,128)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25,105)( 26,106)( 27,107)( 28,108)( 29,109)( 30,110)( 31,111)( 32,112)( 33, 50)( 34, 49)( 35, 52)( 36, 51)( 37, 54)( 38, 53)( 39, 56)( 40, 55)( 41, 73)( 42, 74)( 43, 75)( 44, 76)( 45, 77)( 46, 78)( 47, 79)( 48, 80)( 57, 90)( 58, 89)( 59, 92)( 60, 91)( 61, 94)( 62, 93)( 63, 96)( 64, 95)( 65, 82)( 66, 81)( 67, 84)( 68, 83)( 69, 86)( 70, 85)( 71, 88)( 72, 87)(113,114)(115,116)(117,118)(119,120);; 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*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1,
s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(128)!( 1,101)( 2,102)( 3,104)( 4,103)( 5, 97)( 6, 98)( 7,100)( 8, 99)( 9,110)( 10,109)( 11,111)( 12,112)( 13,106)( 14,105)( 15,107)( 16,108)( 17,117)( 18,118)( 19,120)( 20,119)( 21,113)( 22,114)( 23,116)( 24,115)( 25,126)( 26,125)( 27,127)( 28,128)( 29,122)( 30,121)( 31,123)( 32,124)( 33, 69)( 34, 70)( 35, 72)( 36, 71)( 37, 65)( 38, 66)( 39, 68)( 40, 67)( 41, 78)( 42, 77)( 43, 79)( 44, 80)( 45, 74)( 46, 73)( 47, 75)( 48, 76)( 49, 85)( 50, 86)( 51, 88)( 52, 87)( 53, 81)( 54, 82)( 55, 84)( 56, 83)( 57, 94)( 58, 93)( 59, 95)( 60, 96)( 61, 90)( 62, 89)( 63, 91)( 64, 92); s1 := Sym(128)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9, 11)( 10, 12)( 13, 15)( 14, 16)( 17, 28)( 18, 27)( 19, 26)( 20, 25)( 21, 32)( 22, 31)( 23, 30)( 24, 29)( 33, 43)( 34, 44)( 35, 41)( 36, 42)( 37, 47)( 38, 48)( 39, 45)( 40, 46)( 49, 52)( 50, 51)( 53, 56)( 54, 55)( 57, 60)( 58, 59)( 61, 64)( 62, 63)( 65,123)( 66,124)( 67,121)( 68,122)( 69,127)( 70,128)( 71,125)( 72,126)( 73,115)( 74,116)( 75,113)( 76,114)( 77,119)( 78,120)( 79,117)( 80,118)( 81, 99)( 82,100)( 83, 97)( 84, 98)( 85,103)( 86,104)( 87,101)( 88,102)( 89,107)( 90,108)( 91,105)( 92,106)( 93,111)( 94,112)( 95,109)( 96,110); s2 := Sym(128)!( 9,121)( 10,122)( 11,123)( 12,124)( 13,125)( 14,126)( 15,127)( 16,128)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25,105)( 26,106)( 27,107)( 28,108)( 29,109)( 30,110)( 31,111)( 32,112)( 33, 50)( 34, 49)( 35, 52)( 36, 51)( 37, 54)( 38, 53)( 39, 56)( 40, 55)( 41, 73)( 42, 74)( 43, 75)( 44, 76)( 45, 77)( 46, 78)( 47, 79)( 48, 80)( 57, 90)( 58, 89)( 59, 92)( 60, 91)( 61, 94)( 62, 93)( 63, 96)( 64, 95)( 65, 82)( 66, 81)( 67, 84)( 68, 83)( 69, 86)( 70, 85)( 71, 88)( 72, 87)(113,114)(115,116)(117,118)(119,120); poly := sub<Sym(128)|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*s0*s1*s0*s1*s0*s1, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1, s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1 >;
References
None.
to this polytope.