Polytope of Type {2,8,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,3}*192
if this polytope has a name.
Group : SmallGroup(192,1481)
Rank : 4
Schlafli Type : {2,8,3}
Number of vertices, edges, etc : 2, 16, 24, 6
Order of s₀s₁s₂s₃ : 12
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,8,3,2} of size 384
   {2,8,3,4} of size 768
   {2,8,3,6} of size 1152
Vertex Figure Of :
   {2,2,8,3} of size 384
   {3,2,8,3} of size 576
   {4,2,8,3} of size 768
   {5,2,8,3} of size 960
   {6,2,8,3} of size 1152
   {7,2,8,3} of size 1344
   {9,2,8,3} of size 1728
   {10,2,8,3} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,3}*96
   4-fold quotients : {2,4,3}*48
   8-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,8,3}*384, {2,8,6}*384b
   3-fold covers : {2,8,9}*576, {2,24,3}*576, {6,8,3}*576
   4-fold covers : {2,8,3}*768, {4,8,3}*768a, {8,8,3}*768, {2,8,12}*768e, {4,8,6}*768c, {2,8,6}*768f, {2,8,12}*768h
   5-fold covers : {10,8,3}*960, {2,8,15}*960
   6-fold covers : {4,8,9}*1152, {2,8,18}*1152b, {12,8,3}*1152, {4,24,3}*1152, {2,24,6}*1152b, {6,8,6}*1152a, {2,24,6}*1152e
   7-fold covers : {14,8,3}*1344, {2,8,21}*1344
   9-fold covers : {2,8,27}*1728, {18,8,3}*1728, {2,24,9}*1728, {2,24,3}*1728, {6,8,9}*1728, {6,24,3}*1728a, {6,24,3}*1728b
   10-fold covers : {20,8,3}*1920, {4,8,15}*1920, {10,8,6}*1920a, {2,40,6}*1920c, {2,8,30}*1920b
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 3,13)( 4, 9)( 5, 8)( 6,29)( 7,31)(10,14)(11,18)(12,20)(15,17)(16,19)
(21,46)(22,50)(23,45)(24,48)(25,49)(26,47)(27,30)(28,32)(33,41)(34,43)(35,39)
(36,42)(37,44)(38,40);;
s2 := ( 4, 5)( 6, 7)( 8,21)( 9,24)(11,16)(12,15)(13,33)(14,36)(17,39)(18,40)
(19,25)(20,22)(23,44)(26,43)(27,28)(29,45)(30,47)(31,34)(32,37)(35,49)(38,50)
(41,42);;
s3 := ( 3, 7)( 4,16)( 5,12)( 8,20)( 9,19)(10,28)(11,15)(13,31)(14,32)(17,18)
(21,23)(22,44)(24,26)(25,43)(33,35)(34,49)(36,38)(37,50)(39,41)(40,42)(45,46)
(47,48);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3, s1*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(50)!(1,2);
s1 := Sym(50)!( 3,13)( 4, 9)( 5, 8)( 6,29)( 7,31)(10,14)(11,18)(12,20)(15,17)
(16,19)(21,46)(22,50)(23,45)(24,48)(25,49)(26,47)(27,30)(28,32)(33,41)(34,43)
(35,39)(36,42)(37,44)(38,40);
s2 := Sym(50)!( 4, 5)( 6, 7)( 8,21)( 9,24)(11,16)(12,15)(13,33)(14,36)(17,39)
(18,40)(19,25)(20,22)(23,44)(26,43)(27,28)(29,45)(30,47)(31,34)(32,37)(35,49)
(38,50)(41,42);
s3 := Sym(50)!( 3, 7)( 4,16)( 5,12)( 8,20)( 9,19)(10,28)(11,15)(13,31)(14,32)
(17,18)(21,23)(22,44)(24,26)(25,43)(33,35)(34,49)(36,38)(37,50)(39,41)(40,42)
(45,46)(47,48);
poly := sub<Sym(50)|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, s2*s3*s2*s3*s2*s3, s1*s3*s2*s1*s3*s2*s1*s2*s1*s3*s2*s1*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope