Overview
- Group
- SmallGroup(1728,47874)
- Rank
- 5
- Schläfli Type
- {3,2,6,6}
- Vertices, edges, …
- 3, 3, 24, 72, 24
- Order of s0s1s2s3s4
- 12
- 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
24-fold
36-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (2,3);; s1 := (1,2);; s2 := ( 5, 6)( 9,10)(13,14)(16,28)(17,30)(18,29)(19,31)(20,32)(21,34)(22,33)(23,35)(24,36)(25,38)(26,37)(27,39)(41,42)(45,46)(49,50)(52,64)(53,66)(54,65)(55,67)(56,68)(57,70)(58,69)(59,71)(60,72)(61,74)(62,73)(63,75);; s3 := ( 4,16)( 5,17)( 6,19)( 7,18)( 8,24)( 9,25)(10,27)(11,26)(12,20)(13,21)(14,23)(15,22)(30,31)(32,36)(33,37)(34,39)(35,38)(40,52)(41,53)(42,55)(43,54)(44,60)(45,61)(46,63)(47,62)(48,56)(49,57)(50,59)(51,58)(66,67)(68,72)(69,73)(70,75)(71,74);; s4 := ( 4,47)( 5,45)( 6,46)( 7,44)( 8,43)( 9,41)(10,42)(11,40)(12,51)(13,49)(14,50)(15,48)(16,71)(17,69)(18,70)(19,68)(20,67)(21,65)(22,66)(23,64)(24,75)(25,73)(26,74)(27,72)(28,59)(29,57)(30,58)(31,56)(32,55)(33,53)(34,54)(35,52)(36,63)(37,61)(38,62)(39,60);; 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*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s4*s2*s3*s2*s3*s4*s2*s3*s2*s3*s4*s2*s3*s2*s3*s4*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(75)!(2,3); s1 := Sym(75)!(1,2); s2 := Sym(75)!( 5, 6)( 9,10)(13,14)(16,28)(17,30)(18,29)(19,31)(20,32)(21,34)(22,33)(23,35)(24,36)(25,38)(26,37)(27,39)(41,42)(45,46)(49,50)(52,64)(53,66)(54,65)(55,67)(56,68)(57,70)(58,69)(59,71)(60,72)(61,74)(62,73)(63,75); s3 := Sym(75)!( 4,16)( 5,17)( 6,19)( 7,18)( 8,24)( 9,25)(10,27)(11,26)(12,20)(13,21)(14,23)(15,22)(30,31)(32,36)(33,37)(34,39)(35,38)(40,52)(41,53)(42,55)(43,54)(44,60)(45,61)(46,63)(47,62)(48,56)(49,57)(50,59)(51,58)(66,67)(68,72)(69,73)(70,75)(71,74); s4 := Sym(75)!( 4,47)( 5,45)( 6,46)( 7,44)( 8,43)( 9,41)(10,42)(11,40)(12,51)(13,49)(14,50)(15,48)(16,71)(17,69)(18,70)(19,68)(20,67)(21,65)(22,66)(23,64)(24,75)(25,73)(26,74)(27,72)(28,59)(29,57)(30,58)(31,56)(32,55)(33,53)(34,54)(35,52)(36,63)(37,61)(38,62)(39,60); poly := sub<Sym(75)|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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s4*s2*s3*s2*s3*s4*s2*s3*s2*s3*s4*s2*s3*s2*s3*s4*s2*s3 >;