Polytope of Type {8,6,2}

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

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

to this polytope