Overview
- Group
- SmallGroup(1584,672)
- Rank
- 4
- Schläfli Type
- {2,44,6}
- Vertices, edges, …
- 2, 66, 198, 9
- Order of s0s1s2s3
- 44
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
11-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 13)( 5, 12)( 6, 11)( 7, 10)( 8, 9)( 14, 80)( 15, 90)( 16, 89)( 17, 88)( 18, 87)( 19, 86)( 20, 85)( 21, 84)( 22, 83)( 23, 82)( 24, 81)( 25, 58)( 26, 68)( 27, 67)( 28, 66)( 29, 65)( 30, 64)( 31, 63)( 32, 62)( 33, 61)( 34, 60)( 35, 59)( 36, 69)( 37, 79)( 38, 78)( 39, 77)( 40, 76)( 41, 75)( 42, 74)( 43, 73)( 44, 72)( 45, 71)( 46, 70)( 48, 57)( 49, 56)( 50, 55)( 51, 54)( 52, 53)( 92,101)( 93,100)( 94, 99)( 95, 98)( 96, 97);; s2 := ( 3, 4)( 5, 13)( 6, 12)( 7, 11)( 8, 10)( 14, 26)( 15, 25)( 16, 35)( 17, 34)( 18, 33)( 19, 32)( 20, 31)( 21, 30)( 22, 29)( 23, 28)( 24, 27)( 36, 48)( 37, 47)( 38, 57)( 39, 56)( 40, 55)( 41, 54)( 42, 53)( 43, 52)( 44, 51)( 45, 50)( 46, 49)( 58, 59)( 60, 68)( 61, 67)( 62, 66)( 63, 65)( 69, 92)( 70, 91)( 71,101)( 72,100)( 73, 99)( 74, 98)( 75, 97)( 76, 96)( 77, 95)( 78, 94)( 79, 93)( 80, 81)( 82, 90)( 83, 89)( 84, 88)( 85, 87);; s3 := ( 3,47)( 4,48)( 5,49)( 6,50)( 7,51)( 8,52)( 9,53)(10,54)(11,55)(12,56)(13,57)(14,36)(15,37)(16,38)(17,39)(18,40)(19,41)(20,42)(21,43)(22,44)(23,45)(24,46)(25,58)(26,59)(27,60)(28,61)(29,62)(30,63)(31,64)(32,65)(33,66)(34,67)(35,68)(69,80)(70,81)(71,82)(72,83)(73,84)(74,85)(75,86)(76,87)(77,88)(78,89)(79,90);; 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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*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*s3*s2*s1*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(101)!(1,2); s1 := Sym(101)!( 4, 13)( 5, 12)( 6, 11)( 7, 10)( 8, 9)( 14, 80)( 15, 90)( 16, 89)( 17, 88)( 18, 87)( 19, 86)( 20, 85)( 21, 84)( 22, 83)( 23, 82)( 24, 81)( 25, 58)( 26, 68)( 27, 67)( 28, 66)( 29, 65)( 30, 64)( 31, 63)( 32, 62)( 33, 61)( 34, 60)( 35, 59)( 36, 69)( 37, 79)( 38, 78)( 39, 77)( 40, 76)( 41, 75)( 42, 74)( 43, 73)( 44, 72)( 45, 71)( 46, 70)( 48, 57)( 49, 56)( 50, 55)( 51, 54)( 52, 53)( 92,101)( 93,100)( 94, 99)( 95, 98)( 96, 97); s2 := Sym(101)!( 3, 4)( 5, 13)( 6, 12)( 7, 11)( 8, 10)( 14, 26)( 15, 25)( 16, 35)( 17, 34)( 18, 33)( 19, 32)( 20, 31)( 21, 30)( 22, 29)( 23, 28)( 24, 27)( 36, 48)( 37, 47)( 38, 57)( 39, 56)( 40, 55)( 41, 54)( 42, 53)( 43, 52)( 44, 51)( 45, 50)( 46, 49)( 58, 59)( 60, 68)( 61, 67)( 62, 66)( 63, 65)( 69, 92)( 70, 91)( 71,101)( 72,100)( 73, 99)( 74, 98)( 75, 97)( 76, 96)( 77, 95)( 78, 94)( 79, 93)( 80, 81)( 82, 90)( 83, 89)( 84, 88)( 85, 87); s3 := Sym(101)!( 3,47)( 4,48)( 5,49)( 6,50)( 7,51)( 8,52)( 9,53)(10,54)(11,55)(12,56)(13,57)(14,36)(15,37)(16,38)(17,39)(18,40)(19,41)(20,42)(21,43)(22,44)(23,45)(24,46)(25,58)(26,59)(27,60)(28,61)(29,62)(30,63)(31,64)(32,65)(33,66)(34,67)(35,68)(69,80)(70,81)(71,82)(72,83)(73,84)(74,85)(75,86)(76,87)(77,88)(78,89)(79,90); poly := sub<Sym(101)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*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*s3*s2*s1*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;