Overview
- Group
- SmallGroup(1728,14461)
- Rank
- 5
- Schläfli Type
- {3,2,36,4}
- Vertices, edges, …
- 3, 3, 36, 72, 4
- Order of s0s1s2s3s4
- 36
- 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)( 7,11)( 8,10)( 9,12)(14,15)(16,20)(17,19)(18,21)(23,24)(25,29)(26,28)(27,30)(32,33)(34,38)(35,37)(36,39)(40,58)(41,60)(42,59)(43,65)(44,64)(45,66)(46,62)(47,61)(48,63)(49,67)(50,69)(51,68)(52,74)(53,73)(54,75)(55,71)(56,70)(57,72);; s3 := ( 4,43)( 5,45)( 6,44)( 7,40)( 8,42)( 9,41)(10,47)(11,46)(12,48)(13,52)(14,54)(15,53)(16,49)(17,51)(18,50)(19,56)(20,55)(21,57)(22,61)(23,63)(24,62)(25,58)(26,60)(27,59)(28,65)(29,64)(30,66)(31,70)(32,72)(33,71)(34,67)(35,69)(36,68)(37,74)(38,73)(39,75);; s4 := (40,49)(41,50)(42,51)(43,52)(44,53)(45,54)(46,55)(47,56)(48,57)(58,67)(59,68)(60,69)(61,70)(62,71)(63,72)(64,73)(65,74)(66,75);; 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*s2*s3*s4*s3,
s3*s4*s3*s4*s3*s4*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*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(75)!(2,3); s1 := Sym(75)!(1,2); s2 := Sym(75)!( 5, 6)( 7,11)( 8,10)( 9,12)(14,15)(16,20)(17,19)(18,21)(23,24)(25,29)(26,28)(27,30)(32,33)(34,38)(35,37)(36,39)(40,58)(41,60)(42,59)(43,65)(44,64)(45,66)(46,62)(47,61)(48,63)(49,67)(50,69)(51,68)(52,74)(53,73)(54,75)(55,71)(56,70)(57,72); s3 := Sym(75)!( 4,43)( 5,45)( 6,44)( 7,40)( 8,42)( 9,41)(10,47)(11,46)(12,48)(13,52)(14,54)(15,53)(16,49)(17,51)(18,50)(19,56)(20,55)(21,57)(22,61)(23,63)(24,62)(25,58)(26,60)(27,59)(28,65)(29,64)(30,66)(31,70)(32,72)(33,71)(34,67)(35,69)(36,68)(37,74)(38,73)(39,75); s4 := Sym(75)!(40,49)(41,50)(42,51)(43,52)(44,53)(45,54)(46,55)(47,56)(48,57)(58,67)(59,68)(60,69)(61,70)(62,71)(63,72)(64,73)(65,74)(66,75); 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*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*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*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;