Overview
- Group
- SmallGroup(768,323571)
- Rank
- 4
- Schläfli Type
- {8,12,2}
- Vertices, edges, …
- 16, 96, 24, 2
- 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 := ( 1,73)( 2,74)( 3,75)( 4,76)( 5,77)( 6,78)( 7,79)( 8,80)( 9,81)(10,82)(11,83)(12,84)(13,94)(14,95)(15,96)(16,91)(17,92)(18,93)(19,88)(20,89)(21,90)(22,85)(23,86)(24,87)(25,49)(26,50)(27,51)(28,52)(29,53)(30,54)(31,55)(32,56)(33,57)(34,58)(35,59)(36,60)(37,70)(38,71)(39,72)(40,67)(41,68)(42,69)(43,64)(44,65)(45,66)(46,61)(47,62)(48,63);; s1 := ( 2, 3)( 5, 6)( 7,10)( 8,12)( 9,11)(14,15)(17,18)(19,22)(20,24)(21,23)(25,37)(26,39)(27,38)(28,40)(29,42)(30,41)(31,46)(32,48)(33,47)(34,43)(35,45)(36,44)(50,51)(53,54)(55,58)(56,60)(57,59)(62,63)(65,66)(67,70)(68,72)(69,71)(73,85)(74,87)(75,86)(76,88)(77,90)(78,89)(79,94)(80,96)(81,95)(82,91)(83,93)(84,92);; s2 := ( 1,50)( 2,49)( 3,51)( 4,53)( 5,52)( 6,54)( 7,56)( 8,55)( 9,57)(10,59)(11,58)(12,60)(13,71)(14,70)(15,72)(16,68)(17,67)(18,69)(19,65)(20,64)(21,66)(22,62)(23,61)(24,63)(25,74)(26,73)(27,75)(28,77)(29,76)(30,78)(31,80)(32,79)(33,81)(34,83)(35,82)(36,84)(37,95)(38,94)(39,96)(40,92)(41,91)(42,93)(43,89)(44,88)(45,90)(46,86)(47,85)(48,87);; s3 := (97,98);; 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*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(98)!( 1,73)( 2,74)( 3,75)( 4,76)( 5,77)( 6,78)( 7,79)( 8,80)( 9,81)(10,82)(11,83)(12,84)(13,94)(14,95)(15,96)(16,91)(17,92)(18,93)(19,88)(20,89)(21,90)(22,85)(23,86)(24,87)(25,49)(26,50)(27,51)(28,52)(29,53)(30,54)(31,55)(32,56)(33,57)(34,58)(35,59)(36,60)(37,70)(38,71)(39,72)(40,67)(41,68)(42,69)(43,64)(44,65)(45,66)(46,61)(47,62)(48,63); s1 := Sym(98)!( 2, 3)( 5, 6)( 7,10)( 8,12)( 9,11)(14,15)(17,18)(19,22)(20,24)(21,23)(25,37)(26,39)(27,38)(28,40)(29,42)(30,41)(31,46)(32,48)(33,47)(34,43)(35,45)(36,44)(50,51)(53,54)(55,58)(56,60)(57,59)(62,63)(65,66)(67,70)(68,72)(69,71)(73,85)(74,87)(75,86)(76,88)(77,90)(78,89)(79,94)(80,96)(81,95)(82,91)(83,93)(84,92); s2 := Sym(98)!( 1,50)( 2,49)( 3,51)( 4,53)( 5,52)( 6,54)( 7,56)( 8,55)( 9,57)(10,59)(11,58)(12,60)(13,71)(14,70)(15,72)(16,68)(17,67)(18,69)(19,65)(20,64)(21,66)(22,62)(23,61)(24,63)(25,74)(26,73)(27,75)(28,77)(29,76)(30,78)(31,80)(32,79)(33,81)(34,83)(35,82)(36,84)(37,95)(38,94)(39,96)(40,92)(41,91)(42,93)(43,89)(44,88)(45,90)(46,86)(47,85)(48,87); s3 := Sym(98)!(97,98); 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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*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 >;