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