Overview
- Group
- SmallGroup(1728,47847)
- Rank
- 4
- Schläfli Type
- {4,12,4}
- Vertices, edges, …
- 4, 108, 108, 18
- 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=<s1*s2*(s3*(s2*s1)^2)^2*s3> of order 2
9 facets
- 9 of {4,12}*96b
4 vertex figures
- 4 of 2-fold non-regular quotient of {12,4}*432b
P/N, where N=<(s1*s2)^6> of order 2
10 facets
- 2 of {4,6}*48c
- 8 of {4,12}*96b
4 vertex figures
- 4 of 2-fold non-regular quotient of {12,4}*432b
P/N, where N=<(s1*s2*s3*s2)^2> of order 3
6 facets
- 6 of {4,12}*96b
4 vertex figures
- 4 of 3-fold non-regular quotient of {12,4}*432b
P/N, where N=<s2*s3*(s2*s1)^2*s3*s2*s1*s2*s3, (s1*s2)^6> of order 4
5 facets
- 1 of {4,6}*48c
- 4 of {4,12}*96b
4 vertex figures
- 4 of 4-fold non-regular quotient of {12,4}*432b
P/N, where N=<(s1*s2*s3*s2)^2, s3*s2*s1*s2*s3*s2*s1*s3*s2*s3> of order 6
4 facets
- 2 of {4,6}*48c
- 2 of {4,12}*96b
4 vertex figures
- 4 of 6-fold non-regular quotient of {12,4}*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)( 5,29)( 6,30)( 7,32)( 8,31)( 9,21)(10,22)(11,24)(12,23)(13,25)(14,26)(15,28)(16,27)(19,20)(35,36);; s2 := ( 2, 4)( 6, 8)(10,12)(13,33)(14,36)(15,35)(16,34)(17,25)(18,28)(19,27)(20,26)(21,29)(22,32)(23,31)(24,30);; s3 := ( 1,17)( 2,18)( 3,19)( 4,20)( 5,25)( 6,26)( 7,27)( 8,28)(13,29)(14,30)(15,31)(16,32);; 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*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*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)( 5,29)( 6,30)( 7,32)( 8,31)( 9,21)(10,22)(11,24)(12,23)(13,25)(14,26)(15,28)(16,27)(19,20)(35,36); s2 := Sym(36)!( 2, 4)( 6, 8)(10,12)(13,33)(14,36)(15,35)(16,34)(17,25)(18,28)(19,27)(20,26)(21,29)(22,32)(23,31)(24,30); s3 := Sym(36)!( 1,17)( 2,18)( 3,19)( 4,20)( 5,25)( 6,26)( 7,27)( 8,28)(13,29)(14,30)(15,31)(16,32); 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*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 >;
References
None.
to this polytope.