Overview
- Group
- SmallGroup(1728,47874)
- Rank
- 5
- Schläfli Type
- {3,2,12,6}
- Vertices, edges, …
- 3, 3, 24, 72, 12
- Order of s0s1s2s3s4
- 6
- 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 := ( 4, 5)( 6, 7)( 8,13)( 9,12)(10,15)(11,14)(16,17)(18,19)(20,25)(21,24)(22,27)(23,26)(28,29)(30,31)(32,37)(33,36)(34,39)(35,38)(40,41)(42,43)(44,49)(45,48)(46,51)(47,50)(52,53)(54,55)(56,61)(57,60)(58,63)(59,62)(64,65)(66,67)(68,73)(69,72)(70,75)(71,74);; s3 := ( 4, 8)( 5,10)( 6, 9)( 7,11)(13,14)(16,32)(17,34)(18,33)(19,35)(20,28)(21,30)(22,29)(23,31)(24,36)(25,38)(26,37)(27,39)(40,44)(41,46)(42,45)(43,47)(49,50)(52,68)(53,70)(54,69)(55,71)(56,64)(57,66)(58,65)(59,67)(60,72)(61,74)(62,73)(63,75);; s4 := ( 4,52)( 5,53)( 6,55)( 7,54)( 8,60)( 9,61)(10,63)(11,62)(12,56)(13,57)(14,59)(15,58)(16,40)(17,41)(18,43)(19,42)(20,48)(21,49)(22,51)(23,50)(24,44)(25,45)(26,47)(27,46)(28,64)(29,65)(30,67)(31,66)(32,72)(33,73)(34,75)(35,74)(36,68)(37,69)(38,71)(39,70);; 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*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3*s2*s3*s4*s2*s3,
s4*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s4*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(75)!(2,3); s1 := Sym(75)!(1,2); s2 := Sym(75)!( 4, 5)( 6, 7)( 8,13)( 9,12)(10,15)(11,14)(16,17)(18,19)(20,25)(21,24)(22,27)(23,26)(28,29)(30,31)(32,37)(33,36)(34,39)(35,38)(40,41)(42,43)(44,49)(45,48)(46,51)(47,50)(52,53)(54,55)(56,61)(57,60)(58,63)(59,62)(64,65)(66,67)(68,73)(69,72)(70,75)(71,74); s3 := Sym(75)!( 4, 8)( 5,10)( 6, 9)( 7,11)(13,14)(16,32)(17,34)(18,33)(19,35)(20,28)(21,30)(22,29)(23,31)(24,36)(25,38)(26,37)(27,39)(40,44)(41,46)(42,45)(43,47)(49,50)(52,68)(53,70)(54,69)(55,71)(56,64)(57,66)(58,65)(59,67)(60,72)(61,74)(62,73)(63,75); s4 := Sym(75)!( 4,52)( 5,53)( 6,55)( 7,54)( 8,60)( 9,61)(10,63)(11,62)(12,56)(13,57)(14,59)(15,58)(16,40)(17,41)(18,43)(19,42)(20,48)(21,49)(22,51)(23,50)(24,44)(25,45)(26,47)(27,46)(28,64)(29,65)(30,67)(31,66)(32,72)(33,73)(34,75)(35,74)(36,68)(37,69)(38,71)(39,70); 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*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3*s2*s3*s4*s2*s3, s4*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s4*s3*s2 >;