Overview
- Group
- SmallGroup(1728,37586)
- Rank
- 5
- Schläfli Type
- {3,2,12,12}
- Vertices, edges, …
- 3, 3, 12, 72, 12
- 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
9-fold
12-fold
18-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 := ( 7,10)( 8,11)( 9,12)(16,19)(17,20)(18,21)(25,28)(26,29)(27,30)(34,37)(35,38)(36,39)(40,58)(41,59)(42,60)(43,64)(44,65)(45,66)(46,61)(47,62)(48,63)(49,67)(50,68)(51,69)(52,73)(53,74)(54,75)(55,70)(56,71)(57,72);; s3 := ( 4,43)( 5,45)( 6,44)( 7,40)( 8,42)( 9,41)(10,46)(11,48)(12,47)(13,52)(14,54)(15,53)(16,49)(17,51)(18,50)(19,55)(20,57)(21,56)(22,61)(23,63)(24,62)(25,58)(26,60)(27,59)(28,64)(29,66)(30,65)(31,70)(32,72)(33,71)(34,67)(35,69)(36,68)(37,73)(38,75)(39,74);; s4 := ( 4, 5)( 7,11)( 8,10)( 9,12)(13,14)(16,20)(17,19)(18,21)(22,23)(25,29)(26,28)(27,30)(31,32)(34,38)(35,37)(36,39)(40,68)(41,67)(42,69)(43,74)(44,73)(45,75)(46,71)(47,70)(48,72)(49,59)(50,58)(51,60)(52,65)(53,64)(54,66)(55,62)(56,61)(57,63);; 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*s2*s3*s2*s3*s4*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(75)!(2,3); s1 := Sym(75)!(1,2); s2 := Sym(75)!( 7,10)( 8,11)( 9,12)(16,19)(17,20)(18,21)(25,28)(26,29)(27,30)(34,37)(35,38)(36,39)(40,58)(41,59)(42,60)(43,64)(44,65)(45,66)(46,61)(47,62)(48,63)(49,67)(50,68)(51,69)(52,73)(53,74)(54,75)(55,70)(56,71)(57,72); s3 := Sym(75)!( 4,43)( 5,45)( 6,44)( 7,40)( 8,42)( 9,41)(10,46)(11,48)(12,47)(13,52)(14,54)(15,53)(16,49)(17,51)(18,50)(19,55)(20,57)(21,56)(22,61)(23,63)(24,62)(25,58)(26,60)(27,59)(28,64)(29,66)(30,65)(31,70)(32,72)(33,71)(34,67)(35,69)(36,68)(37,73)(38,75)(39,74); s4 := Sym(75)!( 4, 5)( 7,11)( 8,10)( 9,12)(13,14)(16,20)(17,19)(18,21)(22,23)(25,29)(26,28)(27,30)(31,32)(34,38)(35,37)(36,39)(40,68)(41,67)(42,69)(43,74)(44,73)(45,75)(46,71)(47,70)(48,72)(49,59)(50,58)(51,60)(52,65)(53,64)(54,66)(55,62)(56,61)(57,63); 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*s2*s3*s2*s3*s4*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;