Overview
- Group
- SmallGroup(768,1089270)
- Rank
- 4
- Schläfli Type
- {2,24,6}
- Vertices, edges, …
- 2, 32, 96, 8
- Order of s0s1s2s3
- 8
- 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
4-fold
8-fold
12-fold
16-fold
24-fold
48-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(16,17)(19,23)(20,25)(21,24)(22,26)(27,39)(28,41)(29,40)(30,42)(31,47)(32,49)(33,48)(34,50)(35,43)(36,45)(37,44)(38,46)(51,75)(52,77)(53,76)(54,78)(55,83)(56,85)(57,84)(58,86)(59,79)(60,81)(61,80)(62,82)(63,87)(64,89)(65,88)(66,90)(67,95)(68,97)(69,96)(70,98)(71,91)(72,93)(73,92)(74,94);; s2 := ( 3,55)( 4,56)( 5,58)( 6,57)( 7,51)( 8,52)( 9,54)(10,53)(11,59)(12,60)(13,62)(14,61)(15,67)(16,68)(17,70)(18,69)(19,63)(20,64)(21,66)(22,65)(23,71)(24,72)(25,74)(26,73)(27,91)(28,92)(29,94)(30,93)(31,87)(32,88)(33,90)(34,89)(35,95)(36,96)(37,98)(38,97)(39,79)(40,80)(41,82)(42,81)(43,75)(44,76)(45,78)(46,77)(47,83)(48,84)(49,86)(50,85);; s3 := ( 3, 6)( 7,14)( 8,12)( 9,13)(10,11)(15,18)(19,26)(20,24)(21,25)(22,23)(27,30)(31,38)(32,36)(33,37)(34,35)(39,42)(43,50)(44,48)(45,49)(46,47)(51,54)(55,62)(56,60)(57,61)(58,59)(63,66)(67,74)(68,72)(69,73)(70,71)(75,78)(79,86)(80,84)(81,85)(82,83)(87,90)(91,98)(92,96)(93,97)(94,95);; 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,
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(98)!(1,2); s1 := Sym(98)!( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(16,17)(19,23)(20,25)(21,24)(22,26)(27,39)(28,41)(29,40)(30,42)(31,47)(32,49)(33,48)(34,50)(35,43)(36,45)(37,44)(38,46)(51,75)(52,77)(53,76)(54,78)(55,83)(56,85)(57,84)(58,86)(59,79)(60,81)(61,80)(62,82)(63,87)(64,89)(65,88)(66,90)(67,95)(68,97)(69,96)(70,98)(71,91)(72,93)(73,92)(74,94); s2 := Sym(98)!( 3,55)( 4,56)( 5,58)( 6,57)( 7,51)( 8,52)( 9,54)(10,53)(11,59)(12,60)(13,62)(14,61)(15,67)(16,68)(17,70)(18,69)(19,63)(20,64)(21,66)(22,65)(23,71)(24,72)(25,74)(26,73)(27,91)(28,92)(29,94)(30,93)(31,87)(32,88)(33,90)(34,89)(35,95)(36,96)(37,98)(38,97)(39,79)(40,80)(41,82)(42,81)(43,75)(44,76)(45,78)(46,77)(47,83)(48,84)(49,86)(50,85); s3 := Sym(98)!( 3, 6)( 7,14)( 8,12)( 9,13)(10,11)(15,18)(19,26)(20,24)(21,25)(22,23)(27,30)(31,38)(32,36)(33,37)(34,35)(39,42)(43,50)(44,48)(45,49)(46,47)(51,54)(55,62)(56,60)(57,61)(58,59)(63,66)(67,74)(68,72)(69,73)(70,71)(75,78)(79,86)(80,84)(81,85)(82,83)(87,90)(91,98)(92,96)(93,97)(94,95); poly := sub<Sym(98)|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, s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2 >;