Overview
- Group
- SmallGroup(1728,47847)
- Rank
- 4
- Schläfli Type
- {4,12,4}
- Vertices, edges, …
- 18, 108, 108, 4
- Order of s0s1s2s3
- 6
- Order of s0s1s2s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Universal
- Non-Orientable
- Flat
Quotients maximal quotients in bold
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=<(s0*(s2*s1)^2)^2*s0*s1*s2> of order 2
4 facets
- 4 of 2-fold non-regular quotient of {4,12}*432b
9 vertex figures
- 9 of {12,4}*96b
P/N, where N=<(s0*s1)^2> of order 2
4 facets
- 4 of 2-fold non-regular quotient of {4,12}*432b
10 vertex figures
- 8 of {12,4}*96b
- 2 of {6,4}*48c
P/N, where N=<(s0*s1*s2*s1)^2> of order 3
4 facets
- 4 of 3-fold non-regular quotient of {4,12}*432b
6 vertex figures
- 6 of {12,4}*96b
P/N, where N=<(s0*s1)^2, s0*s2*s1*s0*s1*s2*s1*s0*(s2*s1)^2*s2> of order 4
4 facets
- 4 of 4-fold non-regular quotient of {4,12}*432b
5 vertex figures
- 4 of {12,4}*96b
- 1 of {6,4}*48c
P/N, where N=<(s0*s1)^2, (s0*s1*s2*s1)^2> of order 6
4 facets
- 4 of 6-fold non-regular quotient of {4,12}*432b
4 vertex figures
- 2 of {12,4}*96b
- 2 of {6,4}*48c
Representations
Permutation Representation (GAP)
s0 := ( 5,29)( 6,30)( 7,31)( 8,32)( 9,21)(10,22)(11,23)(12,24)(13,25)(14,26)(15,27)(16,28);; s1 := ( 3, 4)( 7, 8)(11,12)(13,33)(14,34)(15,36)(16,35)(17,25)(18,26)(19,28)(20,27)(21,29)(22,30)(23,32)(24,31);; s2 := ( 1,17)( 2,20)( 3,19)( 4,18)( 5,25)( 6,28)( 7,27)( 8,26)(10,12)(13,29)(14,32)(15,31)(16,30)(22,24)(34,36);; 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*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*s2*s3*s2*s1*s2,
s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
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)!( 5,29)( 6,30)( 7,31)( 8,32)( 9,21)(10,22)(11,23)(12,24)(13,25)(14,26)(15,27)(16,28); s1 := Sym(36)!( 3, 4)( 7, 8)(11,12)(13,33)(14,34)(15,36)(16,35)(17,25)(18,26)(19,28)(20,27)(21,29)(22,30)(23,32)(24,31); s2 := Sym(36)!( 1,17)( 2,20)( 3,19)( 4,18)( 5,25)( 6,28)( 7,27)( 8,26)(10,12)(13,29)(14,32)(15,31)(16,30)(22,24)(34,36); 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*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*s2*s3*s2*s1*s2, s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;
References
None.
to this polytope.