Overview
- Group
- SmallGroup(1728,47887)
- Rank
- 5
- Schläfli Type
- {6,2,4,6}
- Vertices, edges, …
- 6, 6, 12, 36, 18
- Order of s0s1s2s3s4
- 12
- 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
9-fold
18-fold
27-fold
36-fold
54-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (3,4)(5,6);; s1 := (1,5)(2,3)(4,6);; s2 := (10,13)(11,14)(12,15)(19,22)(20,23)(21,24)(28,31)(29,32)(30,33)(37,40)(38,41)(39,42)(43,52)(44,53)(45,54)(46,58)(47,59)(48,60)(49,55)(50,56)(51,57)(61,70)(62,71)(63,72)(64,76)(65,77)(66,78)(67,73)(68,74)(69,75);; s3 := ( 7,43)( 8,46)( 9,49)(10,44)(11,47)(12,50)(13,45)(14,48)(15,51)(16,52)(17,55)(18,58)(19,53)(20,56)(21,59)(22,54)(23,57)(24,60)(25,61)(26,64)(27,67)(28,62)(29,65)(30,68)(31,63)(32,66)(33,69)(34,70)(35,73)(36,76)(37,71)(38,74)(39,77)(40,72)(41,75)(42,78);; s4 := ( 7,35)( 8,34)( 9,36)(10,41)(11,40)(12,42)(13,38)(14,37)(15,39)(16,26)(17,25)(18,27)(19,32)(20,31)(21,33)(22,29)(23,28)(24,30)(43,71)(44,70)(45,72)(46,77)(47,76)(48,78)(49,74)(50,73)(51,75)(52,62)(53,61)(54,63)(55,68)(56,67)(57,69)(58,65)(59,64)(60,66);; 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,
s2*s3*s2*s3*s2*s3*s2*s3, s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(78)!(3,4)(5,6); s1 := Sym(78)!(1,5)(2,3)(4,6); s2 := Sym(78)!(10,13)(11,14)(12,15)(19,22)(20,23)(21,24)(28,31)(29,32)(30,33)(37,40)(38,41)(39,42)(43,52)(44,53)(45,54)(46,58)(47,59)(48,60)(49,55)(50,56)(51,57)(61,70)(62,71)(63,72)(64,76)(65,77)(66,78)(67,73)(68,74)(69,75); s3 := Sym(78)!( 7,43)( 8,46)( 9,49)(10,44)(11,47)(12,50)(13,45)(14,48)(15,51)(16,52)(17,55)(18,58)(19,53)(20,56)(21,59)(22,54)(23,57)(24,60)(25,61)(26,64)(27,67)(28,62)(29,65)(30,68)(31,63)(32,66)(33,69)(34,70)(35,73)(36,76)(37,71)(38,74)(39,77)(40,72)(41,75)(42,78); s4 := Sym(78)!( 7,35)( 8,34)( 9,36)(10,41)(11,40)(12,42)(13,38)(14,37)(15,39)(16,26)(17,25)(18,27)(19,32)(20,31)(21,33)(22,29)(23,28)(24,30)(43,71)(44,70)(45,72)(46,77)(47,76)(48,78)(49,74)(50,73)(51,75)(52,62)(53,61)(54,63)(55,68)(56,67)(57,69)(58,65)(59,64)(60,66); poly := sub<Sym(78)|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, s2*s3*s2*s3*s2*s3*s2*s3, s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;