Overview
- Group
- SmallGroup(576,8659)
- Rank
- 4
- Schläfli Type
- {2,12,6}
- Vertices, edges, …
- 2, 24, 72, 12
- Order of s0s1s2s3
- 6
- 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 := ( 3, 4)( 5, 6)( 7,12)( 8,11)( 9,14)(10,13)(15,16)(17,18)(19,24)(20,23)(21,26)(22,25)(27,28)(29,30)(31,36)(32,35)(33,38)(34,37)(39,40)(41,42)(43,48)(44,47)(45,50)(46,49)(51,52)(53,54)(55,60)(56,59)(57,62)(58,61)(63,64)(65,66)(67,72)(68,71)(69,74)(70,73);; s2 := ( 3, 7)( 4, 9)( 5, 8)( 6,10)(12,13)(15,31)(16,33)(17,32)(18,34)(19,27)(20,29)(21,28)(22,30)(23,35)(24,37)(25,36)(26,38)(39,43)(40,45)(41,44)(42,46)(48,49)(51,67)(52,69)(53,68)(54,70)(55,63)(56,65)(57,64)(58,66)(59,71)(60,73)(61,72)(62,74);; s3 := ( 3,51)( 4,52)( 5,54)( 6,53)( 7,59)( 8,60)( 9,62)(10,61)(11,55)(12,56)(13,58)(14,57)(15,39)(16,40)(17,42)(18,41)(19,47)(20,48)(21,50)(22,49)(23,43)(24,44)(25,46)(26,45)(27,63)(28,64)(29,66)(30,65)(31,71)(32,72)(33,74)(34,73)(35,67)(36,68)(37,70)(38,69);; 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*s2*s1*s2*s3*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2,
s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s3*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(74)!(1,2); s1 := Sym(74)!( 3, 4)( 5, 6)( 7,12)( 8,11)( 9,14)(10,13)(15,16)(17,18)(19,24)(20,23)(21,26)(22,25)(27,28)(29,30)(31,36)(32,35)(33,38)(34,37)(39,40)(41,42)(43,48)(44,47)(45,50)(46,49)(51,52)(53,54)(55,60)(56,59)(57,62)(58,61)(63,64)(65,66)(67,72)(68,71)(69,74)(70,73); s2 := Sym(74)!( 3, 7)( 4, 9)( 5, 8)( 6,10)(12,13)(15,31)(16,33)(17,32)(18,34)(19,27)(20,29)(21,28)(22,30)(23,35)(24,37)(25,36)(26,38)(39,43)(40,45)(41,44)(42,46)(48,49)(51,67)(52,69)(53,68)(54,70)(55,63)(56,65)(57,64)(58,66)(59,71)(60,73)(61,72)(62,74); s3 := Sym(74)!( 3,51)( 4,52)( 5,54)( 6,53)( 7,59)( 8,60)( 9,62)(10,61)(11,55)(12,56)(13,58)(14,57)(15,39)(16,40)(17,42)(18,41)(19,47)(20,48)(21,50)(22,49)(23,43)(24,44)(25,46)(26,45)(27,63)(28,64)(29,66)(30,65)(31,71)(32,72)(33,74)(34,73)(35,67)(36,68)(37,70)(38,69); 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*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2, s3*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s3*s2*s1 >;