Polytope of Type {8,4,3} with group SmallGroup(768,1086052)

Overview

Group: SmallGroup(768,1086052)
Rank: 4
Schläfli Type: {8,4,3}
Vertices, edges, …: 32, 64, 24, 3
Order of s₀s₁s₂s₃: 12
Order of s₀s₁s₂s₃s₂s₁: 8
Also known as: if this polytope has a name.

Special Properties

Universal
Non-Orientable
Flat

Quotients maximal quotients in bold

2-fold

{4,4,3}*384a

4-fold

{4,4,3}*192a

16-fold

{2,4,3}*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*(s1*s0*s2)^3*s1*s2> of order 2

3 facets

3 of 2-fold non-regular quotient of {8,4}*256c

16 vertex figures

16 of {4,3}*24

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References

None.

to this polytope.