Overview
- Group
- SmallGroup(768,1090070)
- Rank
- 4
- Schläfli Type
- {4,6,4}
- Vertices, edges, …
- 16, 48, 48, 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
4-fold
8-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)^2> of order 2
4 facets
- 4 of 2-fold non-regular quotient of {4,6}*192a
8 vertex figures
- 8 of {6,4}*48c
P/N, where N=<(s0*s2*s1)^2*s0*(s1*s2)^2> of order 2
4 facets
- 4 of 2-fold non-regular quotient of {4,6}*192a
8 vertex figures
- 8 of {6,4}*48c
P/N, where N=<(s1*s2)^3> of order 2
4 facets
- 4 of 2-fold non-regular quotient of {4,6}*192a
10 vertex figures
P/N, where N=<(s0*s1)^2, (s0*s2*s1)^2*s0*(s1*s2)^2> of order 4
4 facets
- 4 of 4-fold non-regular quotient of {4,6}*192a
4 vertex figures
- 4 of {6,4}*48c
P/N, where N=<(s0*s1)^2, (s2*s1*s0)^2*(s1*s2)^2> of order 4
4 facets
- 4 of 4-fold non-regular quotient of {4,6}*192a
4 vertex figures
- 4 of {6,4}*48c
P/N, where N=<(s1*s2)^3, (s0*s2*s1)^3> of order 4
4 facets
- 4 of 4-fold non-regular quotient of {4,6}*192a
6 vertex figures
Representations
Permutation Representation (GAP)
s0 := ( 1,13)( 2,14)( 3,15)( 4,16)( 5, 9)( 6,10)( 7,11)( 8,12)(17,29)(18,30)(19,31)(20,32)(21,25)(22,26)(23,27)(24,28)(33,45)(34,46)(35,47)(36,48)(37,41)(38,42)(39,43)(40,44)(49,61)(50,62)(51,63)(52,64)(53,57)(54,58)(55,59)(56,60);; s1 := ( 3, 4)( 5, 6)( 9,16)(10,15)(11,13)(12,14)(19,20)(21,22)(25,32)(26,31)(27,29)(28,30)(33,49)(34,50)(35,52)(36,51)(37,54)(38,53)(39,55)(40,56)(41,64)(42,63)(43,61)(44,62)(45,59)(46,60)(47,58)(48,57);; s2 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,33)(18,35)(19,34)(20,36)(21,41)(22,43)(23,42)(24,44)(25,37)(26,39)(27,38)(28,40)(29,45)(30,47)(31,46)(32,48)(50,51)(53,57)(54,59)(55,58)(56,60)(62,63);; s3 := ( 1,17)( 2,18)( 3,19)( 4,20)( 5,21)( 6,22)( 7,23)( 8,24)( 9,25)(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)(33,49)(34,50)(35,51)(36,52)(37,53)(38,54)(39,55)(40,56)(41,57)(42,58)(43,59)(44,60)(45,61)(46,62)(47,63)(48,64);; 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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(64)!( 1,13)( 2,14)( 3,15)( 4,16)( 5, 9)( 6,10)( 7,11)( 8,12)(17,29)(18,30)(19,31)(20,32)(21,25)(22,26)(23,27)(24,28)(33,45)(34,46)(35,47)(36,48)(37,41)(38,42)(39,43)(40,44)(49,61)(50,62)(51,63)(52,64)(53,57)(54,58)(55,59)(56,60); s1 := Sym(64)!( 3, 4)( 5, 6)( 9,16)(10,15)(11,13)(12,14)(19,20)(21,22)(25,32)(26,31)(27,29)(28,30)(33,49)(34,50)(35,52)(36,51)(37,54)(38,53)(39,55)(40,56)(41,64)(42,63)(43,61)(44,62)(45,59)(46,60)(47,58)(48,57); s2 := Sym(64)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,33)(18,35)(19,34)(20,36)(21,41)(22,43)(23,42)(24,44)(25,37)(26,39)(27,38)(28,40)(29,45)(30,47)(31,46)(32,48)(50,51)(53,57)(54,59)(55,58)(56,60)(62,63); s3 := Sym(64)!( 1,17)( 2,18)( 3,19)( 4,20)( 5,21)( 6,22)( 7,23)( 8,24)( 9,25)(10,26)(11,27)(12,28)(13,29)(14,30)(15,31)(16,32)(33,49)(34,50)(35,51)(36,52)(37,53)(38,54)(39,55)(40,56)(41,57)(42,58)(43,59)(44,60)(45,61)(46,62)(47,63)(48,64); poly := sub<Sym(64)|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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2 >;
References
None.
to this polytope.