Polytope of Type {6,8,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,8,2}*192
if this polytope has a name.
Group : SmallGroup(192,1313)
Rank : 4
Schlafli Type : {6,8,2}
Number of vertices, edges, etc : 6, 24, 8, 2
Order of s₀s₁s₂s₃ : 24
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,8,2,2} of size 384
   {6,8,2,3} of size 576
   {6,8,2,4} of size 768
   {6,8,2,5} of size 960
   {6,8,2,6} of size 1152
   {6,8,2,7} of size 1344
   {6,8,2,9} of size 1728
   {6,8,2,10} of size 1920
Vertex Figure Of :
   {2,6,8,2} of size 384
   {3,6,8,2} of size 576
   {4,6,8,2} of size 768
   {3,6,8,2} of size 768
   {4,6,8,2} of size 768
   {6,6,8,2} of size 1152
   {6,6,8,2} of size 1152
   {6,6,8,2} of size 1152
   {9,6,8,2} of size 1728
   {3,6,8,2} of size 1728
   {10,6,8,2} of size 1920
   {5,6,8,2} of size 1920
   {5,6,8,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,4,2}*96a
   3-fold quotients : {2,8,2}*64
   4-fold quotients : {6,2,2}*48
   6-fold quotients : {2,4,2}*32
   8-fold quotients : {3,2,2}*24
   12-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,8,2}*384a, {6,8,4}*384a, {6,16,2}*384
   3-fold covers : {18,8,2}*576, {6,24,2}*576a, {6,8,6}*576, {6,24,2}*576c
   4-fold covers : {6,8,4}*768a, {12,8,2}*768a, {6,8,8}*768b, {6,8,8}*768c, {24,8,2}*768a, {24,8,2}*768c, {12,8,4}*768d, {6,16,4}*768a, {12,16,2}*768a, {6,16,4}*768b, {12,16,2}*768b, {6,32,2}*768, {6,8,2}*768g
   5-fold covers : {6,40,2}*960, {6,8,10}*960, {30,8,2}*960
   6-fold covers : {18,8,4}*1152a, {36,8,2}*1152a, {6,8,12}*1152a, {12,8,6}*1152a, {6,24,4}*1152a, {6,24,4}*1152c, {12,24,2}*1152a, {12,24,2}*1152c, {18,16,2}*1152, {6,16,6}*1152, {6,48,2}*1152a, {6,48,2}*1152b
   7-fold covers : {6,56,2}*1344, {6,8,14}*1344, {42,8,2}*1344
   9-fold covers : {54,8,2}*1728, {6,72,2}*1728a, {18,24,2}*1728a, {6,24,2}*1728b, {6,8,18}*1728, {18,8,6}*1728, {6,24,6}*1728a, {18,24,2}*1728b, {6,24,2}*1728c, {6,24,6}*1728b, {6,24,6}*1728d, {6,24,2}*1728f, {6,24,6}*1728f, {6,24,6}*1728g, {6,8,6}*1728b, {6,8,2}*1728b
   10-fold covers : {30,8,4}*1920a, {60,8,2}*1920a, {12,8,10}*1920a, {6,8,20}*1920a, {6,40,4}*1920a, {12,40,2}*1920a, {30,16,2}*1920, {6,16,10}*1920, {6,80,2}*1920
Permutation Representation (GAP) :

s0 := ( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(23,24);;
s1 := ( 1, 3)( 2, 9)( 5, 6)( 7,10)( 8,15)(11,12)(13,16)(14,21)(17,18)(19,22)
(20,23);;
s2 := ( 1, 2)( 3, 6)( 4, 7)( 5, 8)( 9,12)(10,13)(11,14)(15,18)(16,19)(17,20)
(21,23)(22,24);;
s3 := (25,26);;
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, 
s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(26)!( 3, 4)( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(23,24);
s1 := Sym(26)!( 1, 3)( 2, 9)( 5, 6)( 7,10)( 8,15)(11,12)(13,16)(14,21)(17,18)
(19,22)(20,23);
s2 := Sym(26)!( 1, 2)( 3, 6)( 4, 7)( 5, 8)( 9,12)(10,13)(11,14)(15,18)(16,19)
(17,20)(21,23)(22,24);
s3 := Sym(26)!(25,26);
poly := sub<Sym(26)|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, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope