Overview
- Group
- SmallGroup(576,6980)
- Rank
- 4
- Schläfli Type
- {2,6,24}
- Vertices, edges, …
- 2, 6, 72, 24
- Order of s0s1s2s3
- 24
- 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
9-fold
12-fold
18-fold
24-fold
36-fold
Covers minimal covers in bold
2-fold
3-fold
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := ( 4, 5)( 6, 9)( 7,11)( 8,10)(13,14)(15,18)(16,20)(17,19)(22,23)(24,27)(25,29)(26,28)(31,32)(33,36)(34,38)(35,37)(40,41)(42,45)(43,47)(44,46)(49,50)(51,54)(52,56)(53,55)(58,59)(60,63)(61,65)(62,64)(67,68)(69,72)(70,74)(71,73);; s2 := ( 3,43)( 4,42)( 5,44)( 6,40)( 7,39)( 8,41)( 9,46)(10,45)(11,47)(12,52)(13,51)(14,53)(15,49)(16,48)(17,50)(18,55)(19,54)(20,56)(21,70)(22,69)(23,71)(24,67)(25,66)(26,68)(27,73)(28,72)(29,74)(30,61)(31,60)(32,62)(33,58)(34,57)(35,59)(36,64)(37,63)(38,65);; s3 := ( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(21,30)(22,31)(23,32)(24,36)(25,37)(26,38)(27,33)(28,34)(29,35)(39,57)(40,58)(41,59)(42,63)(43,64)(44,65)(45,60)(46,61)(47,62)(48,66)(49,67)(50,68)(51,72)(52,73)(53,74)(54,69)(55,70)(56,71);; 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*s3*s2*s3*s1*s2*s1*s2*s3*s2*s3*s1*s2,
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(74)!(1,2); s1 := Sym(74)!( 4, 5)( 6, 9)( 7,11)( 8,10)(13,14)(15,18)(16,20)(17,19)(22,23)(24,27)(25,29)(26,28)(31,32)(33,36)(34,38)(35,37)(40,41)(42,45)(43,47)(44,46)(49,50)(51,54)(52,56)(53,55)(58,59)(60,63)(61,65)(62,64)(67,68)(69,72)(70,74)(71,73); s2 := Sym(74)!( 3,43)( 4,42)( 5,44)( 6,40)( 7,39)( 8,41)( 9,46)(10,45)(11,47)(12,52)(13,51)(14,53)(15,49)(16,48)(17,50)(18,55)(19,54)(20,56)(21,70)(22,69)(23,71)(24,67)(25,66)(26,68)(27,73)(28,72)(29,74)(30,61)(31,60)(32,62)(33,58)(34,57)(35,59)(36,64)(37,63)(38,65); s3 := Sym(74)!( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(21,30)(22,31)(23,32)(24,36)(25,37)(26,38)(27,33)(28,34)(29,35)(39,57)(40,58)(41,59)(42,63)(43,64)(44,65)(45,60)(46,61)(47,62)(48,66)(49,67)(50,68)(51,72)(52,73)(53,74)(54,69)(55,70)(56,71); 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*s3*s2*s3*s1*s2*s1*s2*s3*s2*s3*s1*s2, s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2 >;