Polytope of Type {8,3,3} with group SmallGroup(768,1086051)

Overview

Group: SmallGroup(768,1086051)
Rank: 4
Schläfli Type: {8,3,3}
Vertices, edges, …: 32, 64, 24, 4
Order of s₀s₁s₂s₃: 8
Order of s₀s₁s₂s₃s₂s₁: 8
Also known as: if this polytope has a name.

Special Properties

Orientable
Flat

Quotients maximal quotients in bold

4-fold

{4,3,3}*192

16-fold

{2,3,3}*48

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*s3*s2*(s1*s0)^3*s1*s2*s3> of order 2

4 facets

4 of 2-fold non-regular quotient of {8,3}*192

16 vertex figures

16 of {3,3}*24

P/N, where N=<s0*s3*s2*s1*s0*s1*s2*s3> of order 4

4 facets

2 of 4-fold non-regular quotient of {8,3}*192
2 of 4-fold non-regular quotient of {8,3}*192

8 vertex figures

8 of {3,3}*24

Representations

Permutation Representation (GAP)

s0 := ( 5, 6)( 7, 8)( 9,11)(10,12)(13,16)(14,15)(17,22)(18,21)(19,24)(20,23)(25,32)(26,31)(27,30)(28,29)(33,42)(34,41)(35,44)(36,43)(37,45)(38,46)(39,47)(40,48)(49,64)(50,63)(51,62)(52,61)(53,60)(54,59)(55,58)(56,57);;
s1 := ( 1,33)( 2,36)( 3,35)( 4,34)( 5,46)( 6,47)( 7,48)( 8,45)( 9,41)(10,44)(11,43)(12,42)(13,40)(14,37)(15,38)(16,39)(18,20)(21,30)(22,31)(23,32)(24,29)(26,28)(50,52)(53,62)(54,63)(55,64)(56,61)(58,60);;
s2 := ( 3, 4)( 7, 8)( 9,15)(10,16)(11,14)(12,13)(19,20)(23,24)(25,31)(26,32)(27,30)(28,29)(33,49)(34,50)(35,52)(36,51)(37,53)(38,54)(39,56)(40,55)(41,63)(42,64)(43,62)(44,61)(45,60)(46,59)(47,57)(48,58);;
s3 := ( 2, 4)( 5,13)( 6,16)( 7,15)( 8,14)( 9,11)(17,49)(18,52)(19,51)(20,50)(21,61)(22,64)(23,63)(24,62)(25,59)(26,58)(27,57)(28,60)(29,53)(30,56)(31,55)(32,54)(34,36)(37,45)(38,48)(39,47)(40,46)(41,43);;
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, s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s0*s1*s0*s1*s0*s3*s2*s1*s0*s1*s3*s2*s3*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(64)!( 5, 6)( 7, 8)( 9,11)(10,12)(13,16)(14,15)(17,22)(18,21)(19,24)(20,23)(25,32)(26,31)(27,30)(28,29)(33,42)(34,41)(35,44)(36,43)(37,45)(38,46)(39,47)(40,48)(49,64)(50,63)(51,62)(52,61)(53,60)(54,59)(55,58)(56,57);
s1 := Sym(64)!( 1,33)( 2,36)( 3,35)( 4,34)( 5,46)( 6,47)( 7,48)( 8,45)( 9,41)(10,44)(11,43)(12,42)(13,40)(14,37)(15,38)(16,39)(18,20)(21,30)(22,31)(23,32)(24,29)(26,28)(50,52)(53,62)(54,63)(55,64)(56,61)(58,60);
s2 := Sym(64)!( 3, 4)( 7, 8)( 9,15)(10,16)(11,14)(12,13)(19,20)(23,24)(25,31)(26,32)(27,30)(28,29)(33,49)(34,50)(35,52)(36,51)(37,53)(38,54)(39,56)(40,55)(41,63)(42,64)(43,62)(44,61)(45,60)(46,59)(47,57)(48,58);
s3 := Sym(64)!( 2, 4)( 5,13)( 6,16)( 7,15)( 8,14)( 9,11)(17,49)(18,52)(19,51)(20,50)(21,61)(22,64)(23,63)(24,62)(25,59)(26,58)(27,57)(28,60)(29,53)(30,56)(31,55)(32,54)(34,36)(37,45)(38,48)(39,47)(40,46)(41,43);
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, 
s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s0*s1*s0*s1*s0*s3*s2*s1*s0*s1*s3*s2*s3*s0*s1 >;

References

None.

to this polytope.