Overview
- Group
- SmallGroup(1056,998)
- Rank
- 4
- Schläfli Type
- {4,66,2}
- Vertices, edges, …
- 4, 132, 66, 2
- Order of s0s1s2s3
- 132
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
6-fold
11-fold
12-fold
22-fold
33-fold
44-fold
66-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := ( 67,100)( 68,101)( 69,102)( 70,103)( 71,104)( 72,105)( 73,106)( 74,107)( 75,108)( 76,109)( 77,110)( 78,111)( 79,112)( 80,113)( 81,114)( 82,115)( 83,116)( 84,117)( 85,118)( 86,119)( 87,120)( 88,121)( 89,122)( 90,123)( 91,124)( 92,125)( 93,126)( 94,127)( 95,128)( 96,129)( 97,130)( 98,131)( 99,132);; s1 := ( 1, 67)( 2, 77)( 3, 76)( 4, 75)( 5, 74)( 6, 73)( 7, 72)( 8, 71)( 9, 70)( 10, 69)( 11, 68)( 12, 89)( 13, 99)( 14, 98)( 15, 97)( 16, 96)( 17, 95)( 18, 94)( 19, 93)( 20, 92)( 21, 91)( 22, 90)( 23, 78)( 24, 88)( 25, 87)( 26, 86)( 27, 85)( 28, 84)( 29, 83)( 30, 82)( 31, 81)( 32, 80)( 33, 79)( 34,100)( 35,110)( 36,109)( 37,108)( 38,107)( 39,106)( 40,105)( 41,104)( 42,103)( 43,102)( 44,101)( 45,122)( 46,132)( 47,131)( 48,130)( 49,129)( 50,128)( 51,127)( 52,126)( 53,125)( 54,124)( 55,123)( 56,111)( 57,121)( 58,120)( 59,119)( 60,118)( 61,117)( 62,116)( 63,115)( 64,114)( 65,113)( 66,112);; s2 := ( 1, 13)( 2, 12)( 3, 22)( 4, 21)( 5, 20)( 6, 19)( 7, 18)( 8, 17)( 9, 16)( 10, 15)( 11, 14)( 23, 24)( 25, 33)( 26, 32)( 27, 31)( 28, 30)( 34, 46)( 35, 45)( 36, 55)( 37, 54)( 38, 53)( 39, 52)( 40, 51)( 41, 50)( 42, 49)( 43, 48)( 44, 47)( 56, 57)( 58, 66)( 59, 65)( 60, 64)( 61, 63)( 67, 79)( 68, 78)( 69, 88)( 70, 87)( 71, 86)( 72, 85)( 73, 84)( 74, 83)( 75, 82)( 76, 81)( 77, 80)( 89, 90)( 91, 99)( 92, 98)( 93, 97)( 94, 96)(100,112)(101,111)(102,121)(103,120)(104,119)(105,118)(106,117)(107,116)(108,115)(109,114)(110,113)(122,123)(124,132)(125,131)(126,130)(127,129);; s3 := (133,134);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1,
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*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*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*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*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*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(134)!( 67,100)( 68,101)( 69,102)( 70,103)( 71,104)( 72,105)( 73,106)( 74,107)( 75,108)( 76,109)( 77,110)( 78,111)( 79,112)( 80,113)( 81,114)( 82,115)( 83,116)( 84,117)( 85,118)( 86,119)( 87,120)( 88,121)( 89,122)( 90,123)( 91,124)( 92,125)( 93,126)( 94,127)( 95,128)( 96,129)( 97,130)( 98,131)( 99,132); s1 := Sym(134)!( 1, 67)( 2, 77)( 3, 76)( 4, 75)( 5, 74)( 6, 73)( 7, 72)( 8, 71)( 9, 70)( 10, 69)( 11, 68)( 12, 89)( 13, 99)( 14, 98)( 15, 97)( 16, 96)( 17, 95)( 18, 94)( 19, 93)( 20, 92)( 21, 91)( 22, 90)( 23, 78)( 24, 88)( 25, 87)( 26, 86)( 27, 85)( 28, 84)( 29, 83)( 30, 82)( 31, 81)( 32, 80)( 33, 79)( 34,100)( 35,110)( 36,109)( 37,108)( 38,107)( 39,106)( 40,105)( 41,104)( 42,103)( 43,102)( 44,101)( 45,122)( 46,132)( 47,131)( 48,130)( 49,129)( 50,128)( 51,127)( 52,126)( 53,125)( 54,124)( 55,123)( 56,111)( 57,121)( 58,120)( 59,119)( 60,118)( 61,117)( 62,116)( 63,115)( 64,114)( 65,113)( 66,112); s2 := Sym(134)!( 1, 13)( 2, 12)( 3, 22)( 4, 21)( 5, 20)( 6, 19)( 7, 18)( 8, 17)( 9, 16)( 10, 15)( 11, 14)( 23, 24)( 25, 33)( 26, 32)( 27, 31)( 28, 30)( 34, 46)( 35, 45)( 36, 55)( 37, 54)( 38, 53)( 39, 52)( 40, 51)( 41, 50)( 42, 49)( 43, 48)( 44, 47)( 56, 57)( 58, 66)( 59, 65)( 60, 64)( 61, 63)( 67, 79)( 68, 78)( 69, 88)( 70, 87)( 71, 86)( 72, 85)( 73, 84)( 74, 83)( 75, 82)( 76, 81)( 77, 80)( 89, 90)( 91, 99)( 92, 98)( 93, 97)( 94, 96)(100,112)(101,111)(102,121)(103,120)(104,119)(105,118)(106,117)(107,116)(108,115)(109,114)(110,113)(122,123)(124,132)(125,131)(126,130)(127,129); s3 := Sym(134)!(133,134); poly := sub<Sym(134)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 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*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*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*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*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*s2*s1*s2 >;