Overview
- Group
- SmallGroup(1344,11695)
- Rank
- 5
- Schläfli Type
- {2,2,28,6}
- Vertices, edges, …
- 2, 2, 28, 84, 6
- Order of s0s1s2s3s4
- 42
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
7-fold
14-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (1,2);; s1 := (3,4);; s2 := ( 5, 7)( 6, 8)( 9,31)(10,32)(11,29)(12,30)(13,27)(14,28)(15,25)(16,26)(17,23)(18,24)(19,21)(20,22);; s3 := ( 5, 9)( 6,11)( 7,10)( 8,12)(13,29)(14,31)(15,30)(16,32)(17,25)(18,27)(19,26)(20,28)(22,23);; s4 := ( 6, 8)(10,12)(14,16)(18,20)(22,24)(26,28)(30,32);; 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*s1*s0*s1,
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*s3*s4*s3*s4,
s4*s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*s2*s3,
s2*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s2*s3*s4*s3,
s3*s2*s3*s2*s3*s2*s3*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(32)!(1,2); s1 := Sym(32)!(3,4); s2 := Sym(32)!( 5, 7)( 6, 8)( 9,31)(10,32)(11,29)(12,30)(13,27)(14,28)(15,25)(16,26)(17,23)(18,24)(19,21)(20,22); s3 := Sym(32)!( 5, 9)( 6,11)( 7,10)( 8,12)(13,29)(14,31)(15,30)(16,32)(17,25)(18,27)(19,26)(20,28)(22,23); s4 := Sym(32)!( 6, 8)(10,12)(14,16)(18,20)(22,24)(26,28)(30,32); poly := sub<Sym(32)|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*s1*s0*s1, 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*s3*s4*s3*s4, s4*s2*s3*s4*s3*s4*s2*s3*s4*s2*s3*s4*s3*s4*s2*s3, s2*s3*s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s2*s3*s4*s3, s3*s2*s3*s2*s3*s2*s3*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2 >;