Overview
- Group
- SmallGroup(1944,3579)
- Rank
- 5
- Schläfli Type
- {3,6,6,3}
- Vertices, edges, …
- 3, 27, 54, 27, 3
- Order of s0s1s2s3s4
- 6
- Order of s0s1s2s3s4s3s2s1
- 6
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Orientable
- Flat
- Self-Dual
Quotients maximal quotients in bold
3-fold
9-fold
27-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=<(s2*s3)^2> of order 3
3 facets
- 3 of 3-fold non-regular quotient of {3,6,6}*648e
3 vertex figures
- 2 of 3-fold non-regular quotient of {6,6,3}*648e
- 1 of {6,6,3}*216a
P/N, where N=<(s1*s2)^2> of order 3
3 facets
- 2 of 3-fold non-regular quotient of {3,6,6}*648e
- 1 of {3,6,6}*216a
3 vertex figures
- 3 of 3-fold non-regular quotient of {6,6,3}*648e
Representations
Permutation Representation (GAP)
s0 := ( 2, 3)( 5, 6)( 8, 9)(10,19)(11,21)(12,20)(13,22)(14,24)(15,23)(16,25)(17,27)(18,26);; s1 := ( 1,10)( 2,12)( 3,11)( 4,14)( 5,13)( 6,15)( 7,18)( 8,17)( 9,16)(20,21)(22,23)(25,27);; s2 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)(10,19)(11,21)(12,20)(13,25)(14,27)(15,26)(16,22)(17,24)(18,23);; s3 := ( 1, 4)( 2, 6)( 3, 5)( 8, 9)(10,14)(11,13)(12,15)(16,17)(19,24)(20,23)(21,22)(25,27);; s4 := ( 2, 3)( 4, 7)( 5, 9)( 6, 8)(11,12)(13,16)(14,18)(15,17)(20,21)(22,25)(23,27)(24,26);; 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*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1,
s3*s4*s3*s4*s3*s4, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s3*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(27)!( 2, 3)( 5, 6)( 8, 9)(10,19)(11,21)(12,20)(13,22)(14,24)(15,23)(16,25)(17,27)(18,26); s1 := Sym(27)!( 1,10)( 2,12)( 3,11)( 4,14)( 5,13)( 6,15)( 7,18)( 8,17)( 9,16)(20,21)(22,23)(25,27); s2 := Sym(27)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)(10,19)(11,21)(12,20)(13,25)(14,27)(15,26)(16,22)(17,24)(18,23); s3 := Sym(27)!( 1, 4)( 2, 6)( 3, 5)( 8, 9)(10,14)(11,13)(12,15)(16,17)(19,24)(20,23)(21,22)(25,27); s4 := Sym(27)!( 2, 3)( 4, 7)( 5, 9)( 6, 8)(11,12)(13,16)(14,18)(15,17)(20,21)(22,25)(23,27)(24,26); poly := sub<Sym(27)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s2*s3*s4*s2*s3*s2*s3*s4*s2*s3, s1*s2*s3*s2*s3*s1*s2*s1*s2*s3*s2*s3*s1*s2 >;
References
None.
to this polytope.