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