Overview
- Group
- SmallGroup(1792,1083551)
- Rank
- 3
- Schläfli Type
- {8,7}
- Vertices, edges, …
- 128, 448, 112
- Order of s0s1s2
- 14
- Order of s0s1s2s1
- 8
- Also known as
- if this polytope has a name.
Special Properties
- Compact Hyperbolic Quotient
- Locally Spherical
- Non-Orientable
Quotients maximal quotients in bold
2-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*s0*(s2*s1)^2*s0*(s1*s2)^2> of order 2
56 facets
- 56 of {8}*16
64 vertex figures
- 64 of {7}*14
P/N, where N=<s1*s0*(s2*s1)^2*s0*(s1*s2)^3*s1*s0*s1*s2> of order 2
56 facets
- 56 of {8}*16
64 vertex figures
- 64 of {7}*14
P/N, where N=<s0*s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 2
56 facets
- 56 of {8}*16
64 vertex figures
- 64 of {7}*14
P/N, where N=<s0*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 4
28 facets
- 28 of {8}*16
32 vertex figures
- 32 of {7}*14
P/N, where N=<s0*s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1, s0*s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 4
28 facets
- 28 of {8}*16
32 vertex figures
- 32 of {7}*14
P/N, where N=<(s0*(s1*s2)^2*s1)^2, (s0*s1)^2*s0*(s2*s1)^2*s0*(s1*s2)^2> of order 4
28 facets
- 28 of {8}*16
32 vertex figures
- 32 of {7}*14
P/N, where N=<s1*s2*(s1*s0)^2*(s2*s1)^2*s0*s1*s2, s0*s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 4
28 facets
- 28 of {8}*16
32 vertex figures
- 32 of {7}*14
P/N, where N=<s0*s1*s2*s1*s0*s1*(s2*s1*s0)^2*s1*s2, s0*s2*s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 4
28 facets
- 28 of {8}*16
32 vertex figures
- 32 of {7}*14
Representations
Permutation Representation (GAP)
s0 := ( 1, 23)( 2, 24)( 3, 22)( 4, 21)( 5, 20)( 6, 19)( 7, 17)( 8, 18)( 9, 32)( 10, 31)( 11, 29)( 12, 30)( 13, 27)( 14, 28)( 15, 26)( 16, 25)( 33, 55)( 34, 56)( 35, 54)( 36, 53)( 37, 52)( 38, 51)( 39, 49)( 40, 50)( 41, 64)( 42, 63)( 43, 61)( 44, 62)( 45, 59)( 46, 60)( 47, 58)( 48, 57)( 65, 87)( 66, 88)( 67, 86)( 68, 85)( 69, 84)( 70, 83)( 71, 81)( 72, 82)( 73, 96)( 74, 95)( 75, 93)( 76, 94)( 77, 91)( 78, 92)( 79, 90)( 80, 89)( 97,119)( 98,120)( 99,118)(100,117)(101,116)(102,115)(103,113)(104,114)(105,128)(106,127)(107,125)(108,126)(109,123)(110,124)(111,122)(112,121);; s1 := ( 3, 17)( 4, 18)( 5, 97)( 6, 98)( 7,113)( 8,114)( 9, 33)( 10, 34)( 11, 49)( 12, 50)( 13, 65)( 14, 66)( 15, 81)( 16, 82)( 19, 20)( 21,100)( 22, 99)( 23,115)( 24,116)( 25, 36)( 26, 35)( 27, 51)( 28, 52)( 29, 67)( 30, 68)( 31, 84)( 32, 83)( 37,105)( 38,106)( 39,122)( 40,121)( 43, 58)( 44, 57)( 45, 73)( 46, 74)( 47, 90)( 48, 89)( 53,108)( 54,107)( 55,124)( 56,123)( 59, 60)( 61, 75)( 62, 76)( 63, 91)( 64, 92)( 69,110)( 70,109)( 71,126)( 72,125)( 77, 78)( 79, 94)( 80, 93)( 85,111)( 86,112)( 87,128)( 88,127)(101,102)(103,117)(104,118);; s2 := ( 3, 65)( 4, 66)( 5, 81)( 6, 82)( 7, 17)( 8, 18)( 9, 49)( 10, 50)( 11,113)( 12,114)( 13, 97)( 14, 98)( 15, 33)( 16, 34)( 19, 72)( 20, 71)( 21, 88)( 22, 87)( 25, 56)( 26, 55)( 27,119)( 28,120)( 29,103)( 30,104)( 31, 40)( 32, 39)( 35, 80)( 36, 79)( 37, 95)( 38, 96)( 41, 63)( 42, 64)( 43,128)( 44,127)( 45,111)( 46,112)( 47, 48)( 51, 73)( 52, 74)( 53, 90)( 54, 89)( 57, 58)( 59,122)( 60,121)( 61,105)( 62,106)( 69, 84)( 70, 83)( 75,115)( 76,116)( 77,100)( 78, 99)( 91,117)( 92,118)( 93,102)( 94,101)(107,126)(108,125)(109,110)(123,124);; 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, 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*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,
s2*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(128)!( 1, 23)( 2, 24)( 3, 22)( 4, 21)( 5, 20)( 6, 19)( 7, 17)( 8, 18)( 9, 32)( 10, 31)( 11, 29)( 12, 30)( 13, 27)( 14, 28)( 15, 26)( 16, 25)( 33, 55)( 34, 56)( 35, 54)( 36, 53)( 37, 52)( 38, 51)( 39, 49)( 40, 50)( 41, 64)( 42, 63)( 43, 61)( 44, 62)( 45, 59)( 46, 60)( 47, 58)( 48, 57)( 65, 87)( 66, 88)( 67, 86)( 68, 85)( 69, 84)( 70, 83)( 71, 81)( 72, 82)( 73, 96)( 74, 95)( 75, 93)( 76, 94)( 77, 91)( 78, 92)( 79, 90)( 80, 89)( 97,119)( 98,120)( 99,118)(100,117)(101,116)(102,115)(103,113)(104,114)(105,128)(106,127)(107,125)(108,126)(109,123)(110,124)(111,122)(112,121); s1 := Sym(128)!( 3, 17)( 4, 18)( 5, 97)( 6, 98)( 7,113)( 8,114)( 9, 33)( 10, 34)( 11, 49)( 12, 50)( 13, 65)( 14, 66)( 15, 81)( 16, 82)( 19, 20)( 21,100)( 22, 99)( 23,115)( 24,116)( 25, 36)( 26, 35)( 27, 51)( 28, 52)( 29, 67)( 30, 68)( 31, 84)( 32, 83)( 37,105)( 38,106)( 39,122)( 40,121)( 43, 58)( 44, 57)( 45, 73)( 46, 74)( 47, 90)( 48, 89)( 53,108)( 54,107)( 55,124)( 56,123)( 59, 60)( 61, 75)( 62, 76)( 63, 91)( 64, 92)( 69,110)( 70,109)( 71,126)( 72,125)( 77, 78)( 79, 94)( 80, 93)( 85,111)( 86,112)( 87,128)( 88,127)(101,102)(103,117)(104,118); s2 := Sym(128)!( 3, 65)( 4, 66)( 5, 81)( 6, 82)( 7, 17)( 8, 18)( 9, 49)( 10, 50)( 11,113)( 12,114)( 13, 97)( 14, 98)( 15, 33)( 16, 34)( 19, 72)( 20, 71)( 21, 88)( 22, 87)( 25, 56)( 26, 55)( 27,119)( 28,120)( 29,103)( 30,104)( 31, 40)( 32, 39)( 35, 80)( 36, 79)( 37, 95)( 38, 96)( 41, 63)( 42, 64)( 43,128)( 44,127)( 45,111)( 46,112)( 47, 48)( 51, 73)( 52, 74)( 53, 90)( 54, 89)( 57, 58)( 59,122)( 60,121)( 61,105)( 62,106)( 69, 84)( 70, 83)( 75,115)( 76,116)( 77,100)( 78, 99)( 91,117)( 92,118)( 93,102)( 94,101)(107,126)(108,125)(109,110)(123,124); 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, 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*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, s2*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0 >;
References
None.
to this polytope.