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