Overview
- Group
- SmallGroup(1728,46101)
- Rank
- 4
- Schläfli Type
- {4,6,3}
- Vertices, edges, …
- 16, 144, 108, 9
- Order of s0s1s2s3
- 6
- Order of s0s1s2s3s2s1
- 4
- Also known as
- if this polytope has a name.
Special Properties
- Non-Orientable
- Flat
Quotients maximal quotients in bold
3-fold
Covers minimal covers in bold
None in this atlas.
Irregular Quotients of which this is a minimal cover
Click an entry to reveal its facets and vertex figures.
P/N, where N=<s0*s2*s1*s0*s1*s2> of order 2
9 facets
- 6 of 2-fold non-regular quotient of {4,6}*192a
- 3 of 2-fold non-regular quotient of {4,6}*192a
8 vertex figures
- 8 of {6,3}*108
P/N, where N=<s0*s2*s1*s0*s1*s2, s1*s0*s2*s1*s0*s1*s2*s1> of order 4
9 facets
- 6 of 4-fold non-regular quotient of {4,6}*192a
- 3 of {4,6}*48c
4 vertex figures
- 4 of {6,3}*108
P/N, where N=<s0*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1> of order 4
9 facets
- 9 of 4-fold non-regular quotient of {4,6}*192a
4 vertex figures
- 4 of {6,3}*108
Representations
Permutation Representation (GAP)
s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,16)(14,15)(17,20)(18,19)(21,24)(22,23)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36);; s1 := ( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11)(13,21)(14,23)(15,22)(16,24)(18,19)(25,33)(26,36)(27,35)(28,34)(30,32);; s2 := ( 1,13)( 2,14)( 3,16)( 4,15)( 5,17)( 6,18)( 7,20)( 8,19)( 9,21)(10,22)(11,24)(12,23)(27,28)(31,32)(35,36);; s3 := ( 1,29)( 2,31)( 3,30)( 4,32)( 5,33)( 6,35)( 7,34)( 8,36)( 9,25)(10,27)(11,26)(12,28)(14,15)(18,19)(22,23);; poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s3*s0*s1*s2*s1*s3*s0*s1*s2*s1*s3,
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2,
s1*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(36)!( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,16)(14,15)(17,20)(18,19)(21,24)(22,23)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36); s1 := Sym(36)!( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11)(13,21)(14,23)(15,22)(16,24)(18,19)(25,33)(26,36)(27,35)(28,34)(30,32); s2 := Sym(36)!( 1,13)( 2,14)( 3,16)( 4,15)( 5,17)( 6,18)( 7,20)( 8,19)( 9,21)(10,22)(11,24)(12,23)(27,28)(31,32)(35,36); s3 := Sym(36)!( 1,29)( 2,31)( 3,30)( 4,32)( 5,33)( 6,35)( 7,34)( 8,36)( 9,25)(10,27)(11,26)(12,28)(14,15)(18,19)(22,23); poly := sub<Sym(36)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s3*s0*s1*s2*s1*s3*s0*s1*s2*s1*s3, s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2, s1*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2*s3*s2 >;
References
None.
to this polytope.