Overview
- Group
- SmallGroup(1728,47874)
- Rank
- 6
- Schläfli Type
- {3,2,6,4,3}
- Vertices, edges, …
- 3, 3, 6, 24, 12, 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 := ( 8,12)( 9,13)(10,14)(11,15)(20,24)(21,25)(22,26)(23,27)(32,36)(33,37)(34,38)(35,39)(44,48)(45,49)(46,50)(47,51)(56,60)(57,61)(58,62)(59,63)(68,72)(69,73)(70,74)(71,75);; s3 := ( 4,45)( 5,44)( 6,47)( 7,46)( 8,41)( 9,40)(10,43)(11,42)(12,49)(13,48)(14,51)(15,50)(16,57)(17,56)(18,59)(19,58)(20,53)(21,52)(22,55)(23,54)(24,61)(25,60)(26,63)(27,62)(28,69)(29,68)(30,71)(31,70)(32,65)(33,64)(34,67)(35,66)(36,73)(37,72)(38,75)(39,74);; s4 := ( 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);; s5 := ( 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);; 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,
s4*s5*s4*s5*s4*s5, 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 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(75)!(2,3); s1 := Sym(75)!(1,2); s2 := Sym(75)!( 8,12)( 9,13)(10,14)(11,15)(20,24)(21,25)(22,26)(23,27)(32,36)(33,37)(34,38)(35,39)(44,48)(45,49)(46,50)(47,51)(56,60)(57,61)(58,62)(59,63)(68,72)(69,73)(70,74)(71,75); s3 := Sym(75)!( 4,45)( 5,44)( 6,47)( 7,46)( 8,41)( 9,40)(10,43)(11,42)(12,49)(13,48)(14,51)(15,50)(16,57)(17,56)(18,59)(19,58)(20,53)(21,52)(22,55)(23,54)(24,61)(25,60)(26,63)(27,62)(28,69)(29,68)(30,71)(31,70)(32,65)(33,64)(34,67)(35,66)(36,73)(37,72)(38,75)(39,74); s4 := 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); s5 := 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); 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, s4*s5*s4*s5*s4*s5, 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 >;