Polytope of Type {6,10,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,10,2}*240
if this polytope has a name.
Group : SmallGroup(240,202)
Rank : 4
Schlafli Type : {6,10,2}
Number of vertices, edges, etc : 6, 30, 10, 2
Order of s₀s₁s₂s₃ : 30
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,10,2,2} of size 480
   {6,10,2,3} of size 720
   {6,10,2,4} of size 960
   {6,10,2,5} of size 1200
   {6,10,2,6} of size 1440
   {6,10,2,7} of size 1680
   {6,10,2,8} of size 1920
Vertex Figure Of :
   {2,6,10,2} of size 480
   {3,6,10,2} of size 720
   {4,6,10,2} of size 960
   {3,6,10,2} of size 960
   {4,6,10,2} of size 960
   {6,6,10,2} of size 1440
   {6,6,10,2} of size 1440
   {6,6,10,2} of size 1440
   {8,6,10,2} of size 1920
   {4,6,10,2} of size 1920
   {6,6,10,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,10,2}*80
   5-fold quotients : {6,2,2}*48
   6-fold quotients : {2,5,2}*40
   10-fold quotients : {3,2,2}*24
   15-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,10,2}*480, {6,20,2}*480a, {6,10,4}*480
   3-fold covers : {18,10,2}*720, {6,10,6}*720, {6,30,2}*720a, {6,30,2}*720b
   4-fold covers : {6,20,4}*960, {12,10,4}*960, {24,10,2}*960, {6,40,2}*960, {6,10,8}*960, {12,20,2}*960, {6,20,2}*960c
   5-fold covers : {6,50,2}*1200, {6,10,10}*1200a, {6,10,10}*1200c, {30,10,2}*1200a, {30,10,2}*1200b
   6-fold covers : {36,10,2}*1440, {18,20,2}*1440a, {18,10,4}*1440, {6,10,12}*1440, {12,10,6}*1440, {6,20,6}*1440, {6,60,2}*1440a, {12,30,2}*1440a, {6,30,4}*1440a, {12,30,2}*1440b, {6,60,2}*1440b, {6,30,4}*1440b
   7-fold covers : {6,10,14}*1680, {42,10,2}*1680, {6,70,2}*1680
   8-fold covers : {12,20,4}*1920, {6,20,8}*1920a, {6,40,4}*1920a, {12,40,2}*1920a, {24,20,2}*1920a, {6,20,8}*1920b, {6,40,4}*1920b, {12,40,2}*1920b, {24,20,2}*1920b, {6,20,4}*1920a, {12,20,2}*1920a, {12,10,8}*1920, {24,10,4}*1920, {6,10,16}*1920, {48,10,2}*1920, {6,80,2}*1920, {12,20,2}*1920b, {6,20,2}*1920a, {6,20,4}*1920c, {6,40,2}*1920b, {6,40,2}*1920c, {12,20,2}*1920c
Permutation Representation (GAP) :

s0 := ( 3, 4)( 7, 8)(11,13)(12,14)(17,19)(18,20)(23,25)(24,26)(27,29)(28,30);;
s1 := ( 1, 3)( 2, 7)( 5,12)( 6,11)( 9,18)(10,17)(13,14)(15,24)(16,23)(19,20)
(21,28)(22,27)(25,26)(29,30);;
s2 := ( 1, 9)( 2, 5)( 3,17)( 4,19)( 6,21)( 7,11)( 8,13)(10,15)(12,27)(14,29)
(16,22)(18,23)(20,25)(24,28)(26,30);;
s3 := (31,32);;
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*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(32)!( 3, 4)( 7, 8)(11,13)(12,14)(17,19)(18,20)(23,25)(24,26)(27,29)
(28,30);
s1 := Sym(32)!( 1, 3)( 2, 7)( 5,12)( 6,11)( 9,18)(10,17)(13,14)(15,24)(16,23)
(19,20)(21,28)(22,27)(25,26)(29,30);
s2 := Sym(32)!( 1, 9)( 2, 5)( 3,17)( 4,19)( 6,21)( 7,11)( 8,13)(10,15)(12,27)
(14,29)(16,22)(18,23)(20,25)(24,28)(26,30);
s3 := Sym(32)!(31,32);
poly := sub<Sym(32)|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*s1*s2*s1*s2 >;

to this polytope