Overview
- Group
- SmallGroup(1728,15957)
- Rank
- 5
- Schläfli Type
- {3,2,18,8}
- Vertices, edges, …
- 3, 3, 18, 72, 8
- Order of s0s1s2s3s4
- 72
- 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)(41,42)(43,47)(44,46)(45,48)(50,51)(52,56)(53,55)(54,57)(59,60)(61,65)(62,64)(63,66)(68,69)(70,74)(71,73)(72,75);; s3 := ( 4, 7)( 5, 9)( 6, 8)(10,11)(13,16)(14,18)(15,17)(19,20)(22,34)(23,36)(24,35)(25,31)(26,33)(27,32)(28,38)(29,37)(30,39)(40,61)(41,63)(42,62)(43,58)(44,60)(45,59)(46,65)(47,64)(48,66)(49,70)(50,72)(51,71)(52,67)(53,69)(54,68)(55,74)(56,73)(57,75);; s4 := ( 4,40)( 5,41)( 6,42)( 7,43)( 8,44)( 9,45)(10,46)(11,47)(12,48)(13,49)(14,50)(15,51)(16,52)(17,53)(18,54)(19,55)(20,56)(21,57)(22,67)(23,68)(24,69)(25,70)(26,71)(27,72)(28,73)(29,74)(30,75)(31,58)(32,59)(33,60)(34,61)(35,62)(36,63)(37,64)(38,65)(39,66);; 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*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 ];;
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)(41,42)(43,47)(44,46)(45,48)(50,51)(52,56)(53,55)(54,57)(59,60)(61,65)(62,64)(63,66)(68,69)(70,74)(71,73)(72,75); s3 := Sym(75)!( 4, 7)( 5, 9)( 6, 8)(10,11)(13,16)(14,18)(15,17)(19,20)(22,34)(23,36)(24,35)(25,31)(26,33)(27,32)(28,38)(29,37)(30,39)(40,61)(41,63)(42,62)(43,58)(44,60)(45,59)(46,65)(47,64)(48,66)(49,70)(50,72)(51,71)(52,67)(53,69)(54,68)(55,74)(56,73)(57,75); s4 := Sym(75)!( 4,40)( 5,41)( 6,42)( 7,43)( 8,44)( 9,45)(10,46)(11,47)(12,48)(13,49)(14,50)(15,51)(16,52)(17,53)(18,54)(19,55)(20,56)(21,57)(22,67)(23,68)(24,69)(25,70)(26,71)(27,72)(28,73)(29,74)(30,75)(31,58)(32,59)(33,60)(34,61)(35,62)(36,63)(37,64)(38,65)(39,66); 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*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 >;