Overview
- Group
- SmallGroup(768,1036172)
- Rank
- 5
- Schläfli Type
- {2,24,4,2}
- Vertices, edges, …
- 2, 24, 48, 4, 2
- Order of s0s1s2s3s4
- 24
- Order of s0s1s2s3s4s3s2s1
- 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
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 5)( 7, 8)( 9,12)(10,14)(11,13)(15,18)(16,20)(17,19)(22,23)(25,26)(27,39)(28,41)(29,40)(30,42)(31,44)(32,43)(33,48)(34,50)(35,49)(36,45)(37,47)(38,46)(52,53)(55,56)(57,60)(58,62)(59,61)(63,66)(64,68)(65,67)(70,71)(73,74)(75,87)(76,89)(77,88)(78,90)(79,92)(80,91)(81,96)(82,98)(83,97)(84,93)(85,95)(86,94);; s2 := ( 3,28)( 4,27)( 5,29)( 6,31)( 7,30)( 8,32)( 9,34)(10,33)(11,35)(12,37)(13,36)(14,38)(15,43)(16,42)(17,44)(18,40)(19,39)(20,41)(21,49)(22,48)(23,50)(24,46)(25,45)(26,47)(51,76)(52,75)(53,77)(54,79)(55,78)(56,80)(57,82)(58,81)(59,83)(60,85)(61,84)(62,86)(63,91)(64,90)(65,92)(66,88)(67,87)(68,89)(69,97)(70,96)(71,98)(72,94)(73,93)(74,95);; s3 := ( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)(11,59)(12,60)(13,61)(14,62)(15,66)(16,67)(17,68)(18,63)(19,64)(20,65)(21,72)(22,73)(23,74)(24,69)(25,70)(26,71)(27,81)(28,82)(29,83)(30,84)(31,85)(32,86)(33,75)(34,76)(35,77)(36,78)(37,79)(38,80)(39,96)(40,97)(41,98)(42,93)(43,94)(44,95)(45,90)(46,91)(47,92)(48,87)(49,88)(50,89);; s4 := ( 99,100);; poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3,
s1*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*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*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(100)!(1,2); s1 := Sym(100)!( 4, 5)( 7, 8)( 9,12)(10,14)(11,13)(15,18)(16,20)(17,19)(22,23)(25,26)(27,39)(28,41)(29,40)(30,42)(31,44)(32,43)(33,48)(34,50)(35,49)(36,45)(37,47)(38,46)(52,53)(55,56)(57,60)(58,62)(59,61)(63,66)(64,68)(65,67)(70,71)(73,74)(75,87)(76,89)(77,88)(78,90)(79,92)(80,91)(81,96)(82,98)(83,97)(84,93)(85,95)(86,94); s2 := Sym(100)!( 3,28)( 4,27)( 5,29)( 6,31)( 7,30)( 8,32)( 9,34)(10,33)(11,35)(12,37)(13,36)(14,38)(15,43)(16,42)(17,44)(18,40)(19,39)(20,41)(21,49)(22,48)(23,50)(24,46)(25,45)(26,47)(51,76)(52,75)(53,77)(54,79)(55,78)(56,80)(57,82)(58,81)(59,83)(60,85)(61,84)(62,86)(63,91)(64,90)(65,92)(66,88)(67,87)(68,89)(69,97)(70,96)(71,98)(72,94)(73,93)(74,95); s3 := Sym(100)!( 3,51)( 4,52)( 5,53)( 6,54)( 7,55)( 8,56)( 9,57)(10,58)(11,59)(12,60)(13,61)(14,62)(15,66)(16,67)(17,68)(18,63)(19,64)(20,65)(21,72)(22,73)(23,74)(24,69)(25,70)(26,71)(27,81)(28,82)(29,83)(30,84)(31,85)(32,86)(33,75)(34,76)(35,77)(36,78)(37,79)(38,80)(39,96)(40,97)(41,98)(42,93)(43,94)(44,95)(45,90)(46,91)(47,92)(48,87)(49,88)(50,89); s4 := Sym(100)!( 99,100); poly := sub<Sym(100)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3, s1*s3*s2*s3*s2*s1*s2*s1*s3*s2*s3*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*s2 >;