Overview
- Group
- SmallGroup(1728,33799)
- Rank
- 5
- Schläfli Type
- {24,6,2,3}
- Vertices, edges, …
- 24, 72, 6, 3, 3
- Order of s0s1s2s3s4
- 24
- 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)( 4, 7)( 5, 9)( 6, 8)(11,12)(13,16)(14,18)(15,17)(19,28)(20,30)(21,29)(22,34)(23,36)(24,35)(25,31)(26,33)(27,32)(37,55)(38,57)(39,56)(40,61)(41,63)(42,62)(43,58)(44,60)(45,59)(46,64)(47,66)(48,65)(49,70)(50,72)(51,71)(52,67)(53,69)(54,68);; s1 := ( 1,41)( 2,40)( 3,42)( 4,38)( 5,37)( 6,39)( 7,44)( 8,43)( 9,45)(10,50)(11,49)(12,51)(13,47)(14,46)(15,48)(16,53)(17,52)(18,54)(19,68)(20,67)(21,69)(22,65)(23,64)(24,66)(25,71)(26,70)(27,72)(28,59)(29,58)(30,60)(31,56)(32,55)(33,57)(34,62)(35,61)(36,63);; s2 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)(62,63)(65,66)(68,69)(71,72);; s3 := (74,75);; s4 := (73,74);; 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,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4*s3*s4, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(75)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)(11,12)(13,16)(14,18)(15,17)(19,28)(20,30)(21,29)(22,34)(23,36)(24,35)(25,31)(26,33)(27,32)(37,55)(38,57)(39,56)(40,61)(41,63)(42,62)(43,58)(44,60)(45,59)(46,64)(47,66)(48,65)(49,70)(50,72)(51,71)(52,67)(53,69)(54,68); s1 := Sym(75)!( 1,41)( 2,40)( 3,42)( 4,38)( 5,37)( 6,39)( 7,44)( 8,43)( 9,45)(10,50)(11,49)(12,51)(13,47)(14,46)(15,48)(16,53)(17,52)(18,54)(19,68)(20,67)(21,69)(22,65)(23,64)(24,66)(25,71)(26,70)(27,72)(28,59)(29,58)(30,60)(31,56)(32,55)(33,57)(34,62)(35,61)(36,63); s2 := Sym(75)!( 2, 3)( 5, 6)( 8, 9)(11,12)(14,15)(17,18)(20,21)(23,24)(26,27)(29,30)(32,33)(35,36)(38,39)(41,42)(44,45)(47,48)(50,51)(53,54)(56,57)(59,60)(62,63)(65,66)(68,69)(71,72); s3 := Sym(75)!(74,75); s4 := Sym(75)!(73,74); 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, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;