Polytope of Type {2,8,6}

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

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

to this polytope