Overview
- Group
- SmallGroup(1728,46101)
- Rank
- 4
- Schläfli Type
- {3,6,4}
- Vertices, edges, …
- 9, 108, 144, 16
- 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*(s1*s2)^2*(s3*s2*s1)^2*s0> of order 2
8 facets
- 8 of {3,6}*108
9 vertex figures
- 6 of 2-fold non-regular quotient of {6,4}*192a
- 3 of 2-fold non-regular quotient of {6,4}*192a
P/N, where N=<(s2*s3)^2, (s1*s2)^2*(s3*s2*s1)^2> of order 4
4 facets
- 4 of {3,6}*108
9 vertex figures
- 6 of 4-fold non-regular quotient of {6,4}*192a
- 3 of {6,4}*48c
P/N, where N=<s1*s2*s3*s2*s1*s3, s2*s1*s2*s3*s2*s1*s3*s2*s3> of order 4
4 facets
- 4 of {3,6}*108
9 vertex figures
- 9 of 4-fold non-regular quotient of {6,4}*192a
Representations
Permutation Representation (GAP)
s0 := ( 3, 4)( 7, 8)(11,12)(13,25)(14,26)(15,28)(16,27)(17,29)(18,30)(19,32)(20,31)(21,33)(22,34)(23,36)(24,35);; s1 := ( 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);; s2 := ( 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);; s3 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36);; 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, s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s0*s1*s2*s3*s2*s1*s0*s2*s3*s2*s1*s2*s3*s2,
s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(36)!( 3, 4)( 7, 8)(11,12)(13,25)(14,26)(15,28)(16,27)(17,29)(18,30)(19,32)(20,31)(21,33)(22,34)(23,36)(24,35); s1 := 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); s2 := 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); s3 := Sym(36)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36); 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, s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s0*s1*s2*s3*s2*s1*s0*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;
References
None.
to this polytope.