Overview
- Group
- SmallGroup(1728,47874)
- Rank
- 6
- Schläfli Type
- {3,2,3,4,6}
- Vertices, edges, …
- 3, 3, 6, 12, 24, 6
- Order of s0s1s2s3s4s5
- 6
- Order of s0s1s2s3s4s5s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
3-fold
4-fold
6-fold
8-fold
12-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (2,3);; s1 := (1,2);; s2 := ( 5, 6)( 9,10)(13,14)(16,28)(17,30)(18,29)(19,31)(20,32)(21,34)(22,33)(23,35)(24,36)(25,38)(26,37)(27,39)(41,42)(45,46)(49,50)(52,64)(53,66)(54,65)(55,67)(56,68)(57,70)(58,69)(59,71)(60,72)(61,74)(62,73)(63,75);; s3 := ( 4,16)( 5,17)( 6,19)( 7,18)( 8,20)( 9,21)(10,23)(11,22)(12,24)(13,25)(14,27)(15,26)(30,31)(34,35)(38,39)(40,52)(41,53)(42,55)(43,54)(44,56)(45,57)(46,59)(47,58)(48,60)(49,61)(50,63)(51,62)(66,67)(70,71)(74,75);; s4 := ( 4, 7)( 5, 6)( 8,15)( 9,14)(10,13)(11,12)(16,19)(17,18)(20,27)(21,26)(22,25)(23,24)(28,31)(29,30)(32,39)(33,38)(34,37)(35,36)(40,43)(41,42)(44,51)(45,50)(46,49)(47,48)(52,55)(53,54)(56,63)(57,62)(58,61)(59,60)(64,67)(65,66)(68,75)(69,74)(70,73)(71,72);; s5 := ( 4,44)( 5,45)( 6,46)( 7,47)( 8,40)( 9,41)(10,42)(11,43)(12,48)(13,49)(14,50)(15,51)(16,56)(17,57)(18,58)(19,59)(20,52)(21,53)(22,54)(23,55)(24,60)(25,61)(26,62)(27,63)(28,68)(29,69)(30,70)(31,71)(32,64)(33,65)(34,66)(35,67)(36,72)(37,73)(38,74)(39,75);; poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
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*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4,
s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(75)!(2,3); s1 := Sym(75)!(1,2); s2 := Sym(75)!( 5, 6)( 9,10)(13,14)(16,28)(17,30)(18,29)(19,31)(20,32)(21,34)(22,33)(23,35)(24,36)(25,38)(26,37)(27,39)(41,42)(45,46)(49,50)(52,64)(53,66)(54,65)(55,67)(56,68)(57,70)(58,69)(59,71)(60,72)(61,74)(62,73)(63,75); s3 := Sym(75)!( 4,16)( 5,17)( 6,19)( 7,18)( 8,20)( 9,21)(10,23)(11,22)(12,24)(13,25)(14,27)(15,26)(30,31)(34,35)(38,39)(40,52)(41,53)(42,55)(43,54)(44,56)(45,57)(46,59)(47,58)(48,60)(49,61)(50,63)(51,62)(66,67)(70,71)(74,75); s4 := Sym(75)!( 4, 7)( 5, 6)( 8,15)( 9,14)(10,13)(11,12)(16,19)(17,18)(20,27)(21,26)(22,25)(23,24)(28,31)(29,30)(32,39)(33,38)(34,37)(35,36)(40,43)(41,42)(44,51)(45,50)(46,49)(47,48)(52,55)(53,54)(56,63)(57,62)(58,61)(59,60)(64,67)(65,66)(68,75)(69,74)(70,73)(71,72); s5 := Sym(75)!( 4,44)( 5,45)( 6,46)( 7,47)( 8,40)( 9,41)(10,42)(11,43)(12,48)(13,49)(14,50)(15,51)(16,56)(17,57)(18,58)(19,59)(20,52)(21,53)(22,54)(23,55)(24,60)(25,61)(26,62)(27,63)(28,68)(29,69)(30,70)(31,71)(32,64)(33,65)(34,66)(35,67)(36,72)(37,73)(38,74)(39,75); poly := sub<Sym(75)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 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*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3, s3*s4*s3*s4*s3*s4*s3*s4, s3*s4*s5*s4*s3*s4*s5*s4, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;