Overview
- Group
- SmallGroup(1728,47887)
- Rank
- 5
- Schläfli Type
- {6,2,6,4}
- Vertices, edges, …
- 6, 6, 18, 36, 12
- 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 := ( 7,34)( 8,36)( 9,35)(10,40)(11,42)(12,41)(13,37)(14,39)(15,38)(16,25)(17,27)(18,26)(19,31)(20,33)(21,32)(22,28)(23,30)(24,29)(43,70)(44,72)(45,71)(46,76)(47,78)(48,77)(49,73)(50,75)(51,74)(52,61)(53,63)(54,62)(55,67)(56,69)(57,68)(58,64)(59,66)(60,65);; s3 := ( 7,10)( 8,11)( 9,12)(16,19)(17,20)(18,21)(25,28)(26,29)(27,30)(34,37)(35,38)(36,39)(43,55)(44,56)(45,57)(46,52)(47,53)(48,54)(49,58)(50,59)(51,60)(61,73)(62,74)(63,75)(64,70)(65,71)(66,72)(67,76)(68,77)(69,78);; s4 := ( 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);; 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,
s3*s4*s3*s4*s3*s4*s3*s4, s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
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)!( 7,34)( 8,36)( 9,35)(10,40)(11,42)(12,41)(13,37)(14,39)(15,38)(16,25)(17,27)(18,26)(19,31)(20,33)(21,32)(22,28)(23,30)(24,29)(43,70)(44,72)(45,71)(46,76)(47,78)(48,77)(49,73)(50,75)(51,74)(52,61)(53,63)(54,62)(55,67)(56,69)(57,68)(58,64)(59,66)(60,65); s3 := Sym(78)!( 7,10)( 8,11)( 9,12)(16,19)(17,20)(18,21)(25,28)(26,29)(27,30)(34,37)(35,38)(36,39)(43,55)(44,56)(45,57)(46,52)(47,53)(48,54)(49,58)(50,59)(51,60)(61,73)(62,74)(63,75)(64,70)(65,71)(66,72)(67,76)(68,77)(69,78); s4 := 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); 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, s3*s4*s3*s4*s3*s4*s3*s4, s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;