Overview
- Group
- SmallGroup(1152,153175)
- Rank
- 6
- Schläfli Type
- {2,4,6,6,2}
- Vertices, edges, …
- 2, 4, 12, 18, 6, 2
- Order of s0s1s2s3s4s5
- 12
- 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
9-fold
12-fold
18-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (21,30)(22,31)(23,32)(24,33)(25,34)(26,35)(27,36)(28,37)(29,38);; s2 := ( 3,21)( 4,23)( 5,22)( 6,27)( 7,29)( 8,28)( 9,24)(10,26)(11,25)(12,30)(13,32)(14,31)(15,36)(16,38)(17,37)(18,33)(19,35)(20,34);; s3 := ( 3, 7)( 4, 6)( 5, 8)( 9,10)(12,16)(13,15)(14,17)(18,19)(21,25)(22,24)(23,26)(27,28)(30,34)(31,33)(32,35)(36,37);; s4 := ( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(24,27)(25,28)(26,29)(33,36)(34,37)(35,38);; s5 := (39,40);; 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, 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, s4*s5*s4*s5,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(40)!(1,2); s1 := Sym(40)!(21,30)(22,31)(23,32)(24,33)(25,34)(26,35)(27,36)(28,37)(29,38); s2 := Sym(40)!( 3,21)( 4,23)( 5,22)( 6,27)( 7,29)( 8,28)( 9,24)(10,26)(11,25)(12,30)(13,32)(14,31)(15,36)(16,38)(17,37)(18,33)(19,35)(20,34); s3 := Sym(40)!( 3, 7)( 4, 6)( 5, 8)( 9,10)(12,16)(13,15)(14,17)(18,19)(21,25)(22,24)(23,26)(27,28)(30,34)(31,33)(32,35)(36,37); s4 := Sym(40)!( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(24,27)(25,28)(26,29)(33,36)(34,37)(35,38); s5 := Sym(40)!(39,40); poly := sub<Sym(40)|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, 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, s4*s5*s4*s5, s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3 >;