Polytope of Type {4,8,12} with group SmallGroup(768,201129)

Overview

Group: SmallGroup(768,201129)
Rank: 4
Schläfli Type: {4,8,12}
Vertices, edges, …: 4, 16, 48, 12
Order of s₀s₁s₂s₃: 24
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

2-fold

{4,4,12}*384

3-fold

{4,8,4}*256a

4-fold

6-fold

{4,4,4}*128

8-fold

12-fold

16-fold

24-fold

32-fold

{2,2,3}*24

48-fold

{2,2,2}*16

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

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

Permutation Representation (Magma)

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

References