Overview
- Group
- SmallGroup(1152,157448)
- Rank
- 6
- Schläfli Type
- {2,2,2,9,4}
- Vertices, edges, …
- 2, 2, 2, 18, 36, 8
- Order of s0s1s2s3s4s5
- 18
- Order of s0s1s2s3s4s5s4s3s2s1
- 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
12-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (3,4);; s2 := (5,6);; s3 := ( 8, 9)(11,15)(12,17)(13,16)(14,18)(19,35)(20,37)(21,36)(22,38)(23,31)(24,33)(25,32)(26,34)(27,39)(28,41)(29,40)(30,42)(44,45)(47,51)(48,53)(49,52)(50,54)(55,71)(56,73)(57,72)(58,74)(59,67)(60,69)(61,68)(62,70)(63,75)(64,77)(65,76)(66,78);; s4 := ( 7,19)( 8,20)( 9,22)(10,21)(11,27)(12,28)(13,30)(14,29)(15,23)(16,24)(17,26)(18,25)(31,35)(32,36)(33,38)(34,37)(41,42)(43,55)(44,56)(45,58)(46,57)(47,63)(48,64)(49,66)(50,65)(51,59)(52,60)(53,62)(54,61)(67,71)(68,72)(69,74)(70,73)(77,78);; s5 := ( 7,46)( 8,45)( 9,44)(10,43)(11,50)(12,49)(13,48)(14,47)(15,54)(16,53)(17,52)(18,51)(19,58)(20,57)(21,56)(22,55)(23,62)(24,61)(25,60)(26,59)(27,66)(28,65)(29,64)(30,63)(31,70)(32,69)(33,68)(34,67)(35,74)(36,73)(37,72)(38,71)(39,78)(40,77)(41,76)(42,75);; 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*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*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,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s4*s5*s4*s5*s4*s5*s4*s5,
s3*s4*s3*s4*s5*s4*s3*s4*s3*s4*s5*s4,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(78)!(1,2); s1 := Sym(78)!(3,4); s2 := Sym(78)!(5,6); s3 := Sym(78)!( 8, 9)(11,15)(12,17)(13,16)(14,18)(19,35)(20,37)(21,36)(22,38)(23,31)(24,33)(25,32)(26,34)(27,39)(28,41)(29,40)(30,42)(44,45)(47,51)(48,53)(49,52)(50,54)(55,71)(56,73)(57,72)(58,74)(59,67)(60,69)(61,68)(62,70)(63,75)(64,77)(65,76)(66,78); s4 := Sym(78)!( 7,19)( 8,20)( 9,22)(10,21)(11,27)(12,28)(13,30)(14,29)(15,23)(16,24)(17,26)(18,25)(31,35)(32,36)(33,38)(34,37)(41,42)(43,55)(44,56)(45,58)(46,57)(47,63)(48,64)(49,66)(50,65)(51,59)(52,60)(53,62)(54,61)(67,71)(68,72)(69,74)(70,73)(77,78); s5 := Sym(78)!( 7,46)( 8,45)( 9,44)(10,43)(11,50)(12,49)(13,48)(14,47)(15,54)(16,53)(17,52)(18,51)(19,58)(20,57)(21,56)(22,55)(23,62)(24,61)(25,60)(26,59)(27,66)(28,65)(29,64)(30,63)(31,70)(32,69)(33,68)(34,67)(35,74)(36,73)(37,72)(38,71)(39,78)(40,77)(41,76)(42,75); poly := sub<Sym(78)|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*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*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, s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5*s4*s5*s4*s5, s3*s4*s3*s4*s5*s4*s3*s4*s3*s4*s5*s4, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;