Overview
- Group
- SmallGroup(576,8659)
- Rank
- 4
- Schläfli Type
- {2,6,6}
- Vertices, edges, …
- 2, 24, 72, 24
- 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
24-fold
36-fold
Covers minimal covers in bold
2-fold
3-fold
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(15,27)(16,29)(17,28)(18,30)(19,35)(20,37)(21,36)(22,38)(23,31)(24,33)(25,32)(26,34)(40,41)(43,47)(44,49)(45,48)(46,50)(51,63)(52,65)(53,64)(54,66)(55,71)(56,73)(57,72)(58,74)(59,67)(60,69)(61,68)(62,70);; 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)(15,43)(16,44)(17,46)(18,45)(19,39)(20,40)(21,42)(22,41)(23,47)(24,48)(25,50)(26,49)(27,67)(28,68)(29,70)(30,69)(31,63)(32,64)(33,66)(34,65)(35,71)(36,72)(37,74)(38,73);; s3 := ( 3, 6)( 7,10)(11,14)(15,30)(16,28)(17,29)(18,27)(19,34)(20,32)(21,33)(22,31)(23,38)(24,36)(25,37)(26,35)(39,42)(43,46)(47,50)(51,66)(52,64)(53,65)(54,63)(55,70)(56,68)(57,69)(58,67)(59,74)(60,72)(61,73)(62,71);; 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*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(74)!(1,2); s1 := Sym(74)!( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(15,27)(16,29)(17,28)(18,30)(19,35)(20,37)(21,36)(22,38)(23,31)(24,33)(25,32)(26,34)(40,41)(43,47)(44,49)(45,48)(46,50)(51,63)(52,65)(53,64)(54,66)(55,71)(56,73)(57,72)(58,74)(59,67)(60,69)(61,68)(62,70); s2 := Sym(74)!( 3,55)( 4,56)( 5,58)( 6,57)( 7,51)( 8,52)( 9,54)(10,53)(11,59)(12,60)(13,62)(14,61)(15,43)(16,44)(17,46)(18,45)(19,39)(20,40)(21,42)(22,41)(23,47)(24,48)(25,50)(26,49)(27,67)(28,68)(29,70)(30,69)(31,63)(32,64)(33,66)(34,65)(35,71)(36,72)(37,74)(38,73); s3 := Sym(74)!( 3, 6)( 7,10)(11,14)(15,30)(16,28)(17,29)(18,27)(19,34)(20,32)(21,33)(22,31)(23,38)(24,36)(25,37)(26,35)(39,42)(43,46)(47,50)(51,66)(52,64)(53,65)(54,63)(55,70)(56,68)(57,69)(58,67)(59,74)(60,72)(61,73)(62,71); poly := sub<Sym(74)|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*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2*s3*s1*s2*s3*s2 >;