Overview
- Group
- SmallGroup(1056,917)
- Rank
- 4
- Schläfli Type
- {44,6,2}
- Vertices, edges, …
- 44, 132, 6, 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
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 := ( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 13, 22)( 14, 21)( 15, 20)( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 46, 55)( 47, 54)( 48, 53)( 49, 52)( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 67,100)( 68,110)( 69,109)( 70,108)( 71,107)( 72,106)( 73,105)( 74,104)( 75,103)( 76,102)( 77,101)( 78,111)( 79,121)( 80,120)( 81,119)( 82,118)( 83,117)( 84,116)( 85,115)( 86,114)( 87,113)( 88,112)( 89,122)( 90,132)( 91,131)( 92,130)( 93,129)( 94,128)( 95,127)( 96,126)( 97,125)( 98,124)( 99,123);; s1 := ( 1, 68)( 2, 67)( 3, 77)( 4, 76)( 5, 75)( 6, 74)( 7, 73)( 8, 72)( 9, 71)( 10, 70)( 11, 69)( 12, 90)( 13, 89)( 14, 99)( 15, 98)( 16, 97)( 17, 96)( 18, 95)( 19, 94)( 20, 93)( 21, 92)( 22, 91)( 23, 79)( 24, 78)( 25, 88)( 26, 87)( 27, 86)( 28, 85)( 29, 84)( 30, 83)( 31, 82)( 32, 81)( 33, 80)( 34,101)( 35,100)( 36,110)( 37,109)( 38,108)( 39,107)( 40,106)( 41,105)( 42,104)( 43,103)( 44,102)( 45,123)( 46,122)( 47,132)( 48,131)( 49,130)( 50,129)( 51,128)( 52,127)( 53,126)( 54,125)( 55,124)( 56,112)( 57,111)( 58,121)( 59,120)( 60,119)( 61,118)( 62,117)( 63,116)( 64,115)( 65,114)( 66,113);; s2 := ( 1, 12)( 2, 13)( 3, 14)( 4, 15)( 5, 16)( 6, 17)( 7, 18)( 8, 19)( 9, 20)( 10, 21)( 11, 22)( 34, 45)( 35, 46)( 36, 47)( 37, 48)( 38, 49)( 39, 50)( 40, 51)( 41, 52)( 42, 53)( 43, 54)( 44, 55)( 67, 78)( 68, 79)( 69, 80)( 70, 81)( 71, 82)( 72, 83)( 73, 84)( 74, 85)( 75, 86)( 76, 87)( 77, 88)(100,111)(101,112)(102,113)(103,114)(104,115)(105,116)(106,117)(107,118)(108,119)(109,120)(110,121);; 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*s2*s1*s0*s1*s2*s1, 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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(134)!( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 13, 22)( 14, 21)( 15, 20)( 16, 19)( 17, 18)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)( 35, 44)( 36, 43)( 37, 42)( 38, 41)( 39, 40)( 46, 55)( 47, 54)( 48, 53)( 49, 52)( 50, 51)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 67,100)( 68,110)( 69,109)( 70,108)( 71,107)( 72,106)( 73,105)( 74,104)( 75,103)( 76,102)( 77,101)( 78,111)( 79,121)( 80,120)( 81,119)( 82,118)( 83,117)( 84,116)( 85,115)( 86,114)( 87,113)( 88,112)( 89,122)( 90,132)( 91,131)( 92,130)( 93,129)( 94,128)( 95,127)( 96,126)( 97,125)( 98,124)( 99,123); s1 := Sym(134)!( 1, 68)( 2, 67)( 3, 77)( 4, 76)( 5, 75)( 6, 74)( 7, 73)( 8, 72)( 9, 71)( 10, 70)( 11, 69)( 12, 90)( 13, 89)( 14, 99)( 15, 98)( 16, 97)( 17, 96)( 18, 95)( 19, 94)( 20, 93)( 21, 92)( 22, 91)( 23, 79)( 24, 78)( 25, 88)( 26, 87)( 27, 86)( 28, 85)( 29, 84)( 30, 83)( 31, 82)( 32, 81)( 33, 80)( 34,101)( 35,100)( 36,110)( 37,109)( 38,108)( 39,107)( 40,106)( 41,105)( 42,104)( 43,103)( 44,102)( 45,123)( 46,122)( 47,132)( 48,131)( 49,130)( 50,129)( 51,128)( 52,127)( 53,126)( 54,125)( 55,124)( 56,112)( 57,111)( 58,121)( 59,120)( 60,119)( 61,118)( 62,117)( 63,116)( 64,115)( 65,114)( 66,113); s2 := Sym(134)!( 1, 12)( 2, 13)( 3, 14)( 4, 15)( 5, 16)( 6, 17)( 7, 18)( 8, 19)( 9, 20)( 10, 21)( 11, 22)( 34, 45)( 35, 46)( 36, 47)( 37, 48)( 38, 49)( 39, 50)( 40, 51)( 41, 52)( 42, 53)( 43, 54)( 44, 55)( 67, 78)( 68, 79)( 69, 80)( 70, 81)( 71, 82)( 72, 83)( 73, 84)( 74, 85)( 75, 86)( 76, 87)( 77, 88)(100,111)(101,112)(102,113)(103,114)(104,115)(105,116)(106,117)(107,118)(108,119)(109,120)(110,121); 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*s2*s1*s0*s1*s2*s1, 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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;