Overview
- Group
- SmallGroup(768,323571)
- Rank
- 4
- Schläfli Type
- {2,12,8}
- Vertices, edges, …
- 2, 24, 96, 16
- Order of s0s1s2s3
- 12
- 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
8-fold
12-fold
16-fold
24-fold
32-fold
48-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 3,51)( 4,53)( 5,52)( 6,54)( 7,56)( 8,55)( 9,57)(10,59)(11,58)(12,60)(13,62)(14,61)(15,72)(16,74)(17,73)(18,69)(19,71)(20,70)(21,66)(22,68)(23,67)(24,63)(25,65)(26,64)(27,75)(28,77)(29,76)(30,78)(31,80)(32,79)(33,81)(34,83)(35,82)(36,84)(37,86)(38,85)(39,96)(40,98)(41,97)(42,93)(43,95)(44,94)(45,90)(46,92)(47,91)(48,87)(49,89)(50,88);; s2 := ( 3, 4)( 6, 7)( 9,13)(10,12)(11,14)(15,16)(18,19)(21,25)(22,24)(23,26)(27,40)(28,39)(29,41)(30,43)(31,42)(32,44)(33,49)(34,48)(35,50)(36,46)(37,45)(38,47)(51,52)(54,55)(57,61)(58,60)(59,62)(63,64)(66,67)(69,73)(70,72)(71,74)(75,88)(76,87)(77,89)(78,91)(79,90)(80,92)(81,97)(82,96)(83,98)(84,94)(85,93)(86,95);; s3 := ( 3,75)( 4,76)( 5,77)( 6,78)( 7,79)( 8,80)( 9,81)(10,82)(11,83)(12,84)(13,85)(14,86)(15,96)(16,97)(17,98)(18,93)(19,94)(20,95)(21,90)(22,91)(23,92)(24,87)(25,88)(26,89)(27,51)(28,52)(29,53)(30,54)(31,55)(32,56)(33,57)(34,58)(35,59)(36,60)(37,61)(38,62)(39,72)(40,73)(41,74)(42,69)(43,70)(44,71)(45,66)(46,67)(47,68)(48,63)(49,64)(50,65);; 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*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(98)!(1,2); s1 := Sym(98)!( 3,51)( 4,53)( 5,52)( 6,54)( 7,56)( 8,55)( 9,57)(10,59)(11,58)(12,60)(13,62)(14,61)(15,72)(16,74)(17,73)(18,69)(19,71)(20,70)(21,66)(22,68)(23,67)(24,63)(25,65)(26,64)(27,75)(28,77)(29,76)(30,78)(31,80)(32,79)(33,81)(34,83)(35,82)(36,84)(37,86)(38,85)(39,96)(40,98)(41,97)(42,93)(43,95)(44,94)(45,90)(46,92)(47,91)(48,87)(49,89)(50,88); s2 := Sym(98)!( 3, 4)( 6, 7)( 9,13)(10,12)(11,14)(15,16)(18,19)(21,25)(22,24)(23,26)(27,40)(28,39)(29,41)(30,43)(31,42)(32,44)(33,49)(34,48)(35,50)(36,46)(37,45)(38,47)(51,52)(54,55)(57,61)(58,60)(59,62)(63,64)(66,67)(69,73)(70,72)(71,74)(75,88)(76,87)(77,89)(78,91)(79,90)(80,92)(81,97)(82,96)(83,98)(84,94)(85,93)(86,95); s3 := Sym(98)!( 3,75)( 4,76)( 5,77)( 6,78)( 7,79)( 8,80)( 9,81)(10,82)(11,83)(12,84)(13,85)(14,86)(15,96)(16,97)(17,98)(18,93)(19,94)(20,95)(21,90)(22,91)(23,92)(24,87)(25,88)(26,89)(27,51)(28,52)(29,53)(30,54)(31,55)(32,56)(33,57)(34,58)(35,59)(36,60)(37,61)(38,62)(39,72)(40,73)(41,74)(42,69)(43,70)(44,71)(45,66)(46,67)(47,68)(48,63)(49,64)(50,65); 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*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*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 >;