Polytope of Type {8,6,6} with group SmallGroup(1152,155791)

Overview

Group: SmallGroup(1152,155791)
Rank: 4
Schläfli Type: {8,6,6}
Vertices, edges, …: 16, 48, 36, 6
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

3-fold

{8,6,2}*384a

4-fold

{4,6,6}*288f

8-fold

{4,3,6}*144

12-fold

{4,6,2}*96b

24-fold

{4,3,2}*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)^4> of order 2

6 facets

6 of 2-fold non-regular quotient of {8,6}*192a

8 vertex figures

8 of {6,6}*72c

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

s0 := Sym(48)!( 1, 9)( 2,10)( 3,11)( 4,12)( 5,14)( 6,13)( 7,16)( 8,15)(17,25)(18,26)(19,27)(20,28)(21,30)(22,29)(23,32)(24,31)(33,41)(34,42)(35,43)(36,44)(37,46)(38,45)(39,48)(40,47);
s1 := Sym(48)!( 3, 4)( 5, 6)( 9,13)(10,14)(11,16)(12,15)(17,33)(18,34)(19,36)(20,35)(21,38)(22,37)(23,39)(24,40)(25,45)(26,46)(27,48)(28,47)(29,41)(30,42)(31,44)(32,43);
s2 := Sym(48)!( 1,25)( 2,28)( 3,27)( 4,26)( 5,21)( 6,24)( 7,23)( 8,22)( 9,17)(10,20)(11,19)(12,18)(13,31)(14,30)(15,29)(16,32)(33,41)(34,44)(35,43)(36,42)(38,40)(45,47);
s3 := Sym(48)!(17,33)(18,34)(19,35)(20,36)(21,37)(22,38)(23,39)(24,40)(25,41)(26,42)(27,43)(28,44)(29,45)(30,46)(31,47)(32,48);
poly := sub<Sym(48)|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*s2*s0*s1*s2*s0*s1*s2, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References

None.

to this polytope.