Overview
- Group
- SmallGroup(1728,47847)
- Rank
- 4
- Schläfli Type
- {4,6,4}
- Vertices, edges, …
- 4, 108, 108, 36
- Order of s0s1s2s3
- 12
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
9-fold
18-fold
36-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=<(s1*s2)^3> of order 2
21 facets
4 vertex figures
- 4 of 2-fold non-regular quotient of {6,4}*432b
P/N, where N=<((s2*s1)^2*s2*s3)^2> of order 2
18 facets
- 18 of {4,6}*48c
4 vertex figures
- 4 of 2-fold non-regular quotient of {6,4}*432b
P/N, where N=<(s1*s2)^2*(s3*s2*s1)^2*(s2*s3)^2> of order 3
12 facets
- 12 of {4,6}*48c
4 vertex figures
- 4 of 3-fold non-regular quotient of {6,4}*432b
P/N, where N=<(s1*s2*s3*s2)^2> of order 3
12 facets
- 12 of {4,6}*48c
4 vertex figures
- 4 of 3-fold non-regular quotient of {6,4}*432b
P/N, where N=<(s1*s2)^3, s1*s3*(s2*s1)^2*s2*s3> of order 4
12 facets
4 vertex figures
- 4 of 4-fold non-regular quotient of {6,4}*432b
P/N, where N=<(s1*s2)^3, s2*s3*s2*s1*s3*(s2*s1)^2*s3*s2*s3> of order 6
9 facets
4 vertex figures
- 4 of 6-fold non-regular quotient of {6,4}*432b
P/N, where N=<s3*s2*s1*s2*s3*s2*s1*s3*s2*s3, s1*s2*s3*(s2*s1)^2*s2*s3*s2*s1*s2> of order 6
6 facets
- 6 of {4,6}*48c
4 vertex figures
- 4 of 6-fold non-regular quotient of {6,4}*432b
P/N, where N=<(s2*s3)^2, s1*s2*s3*s2*s1*s3> of order 6
6 facets
- 6 of {4,6}*48c
4 vertex figures
- 4 of 6-fold non-regular quotient of {6,4}*432b
P/N, where N=<(s1*s2)^3, s1*s3*(s2*s1)^2*s2*s3, (s1*s3*s2)^3*s3> of order 12
5 facets
4 vertex figures
- 4 of 12-fold non-regular quotient of {6,4}*432b
Representations
Permutation Representation (GAP)
s0 := ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)(25,27)(26,28)(29,31)(30,32)(33,35)(34,36);; s1 := ( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11)(13,25)(14,26)(15,28)(16,27)(17,33)(18,34)(19,36)(20,35)(21,29)(22,30)(23,32)(24,31);; s2 := ( 1,13)( 2,16)( 3,15)( 4,14)( 6, 8)( 9,33)(10,36)(11,35)(12,34)(17,29)(18,32)(19,31)(20,30)(22,24)(26,28);; s3 := (13,33)(14,34)(15,35)(16,36)(17,25)(18,26)(19,27)(20,28)(21,29)(22,30)(23,31)(24,32);; 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*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*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)(13,15)(14,16)(17,19)(18,20)(21,23)(22,24)(25,27)(26,28)(29,31)(30,32)(33,35)(34,36); s1 := Sym(36)!( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11)(13,25)(14,26)(15,28)(16,27)(17,33)(18,34)(19,36)(20,35)(21,29)(22,30)(23,32)(24,31); s2 := Sym(36)!( 1,13)( 2,16)( 3,15)( 4,14)( 6, 8)( 9,33)(10,36)(11,35)(12,34)(17,29)(18,32)(19,31)(20,30)(22,24)(26,28); s3 := Sym(36)!(13,33)(14,34)(15,35)(16,36)(17,25)(18,26)(19,27)(20,28)(21,29)(22,30)(23,31)(24,32); 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*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s2*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2 >;
References
None.
to this polytope.