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Polytope of Type {2,5,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,5,10}*200
if this polytope has a name.
Group : SmallGroup(200,49)
Rank : 4
Schlafli Type : {2,5,10}
Number of vertices, edges, etc : 2, 5, 25, 10
Order of s0s1s2s3 : 10
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,5,10,2} of size 400
   {2,5,10,4} of size 800
   {2,5,10,5} of size 1000
   {2,5,10,6} of size 1200
   {2,5,10,8} of size 1600
   {2,5,10,10} of size 2000
   {2,5,10,10} of size 2000
Vertex Figure Of :
   {2,2,5,10} of size 400
   {3,2,5,10} of size 600
   {4,2,5,10} of size 800
   {5,2,5,10} of size 1000
   {6,2,5,10} of size 1200
   {7,2,5,10} of size 1400
   {8,2,5,10} of size 1600
   {9,2,5,10} of size 1800
   {10,2,5,10} of size 2000
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,5,2}*40
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,10,10}*400c
   3-fold covers : {2,15,10}*600
   4-fold covers : {2,20,10}*800b, {4,10,10}*800b, {2,10,20}*800c
   5-fold covers : {2,25,10}*1000, {2,5,10}*1000, {10,5,10}*1000
   6-fold covers : {6,10,10}*1200c, {2,10,30}*1200a, {2,30,10}*1200c
   7-fold covers : {2,35,10}*1400
   8-fold covers : {4,20,10}*1600b, {2,40,10}*1600b, {8,10,10}*1600b, {2,20,20}*1600c, {4,10,20}*1600c, {2,10,40}*1600c
   9-fold covers : {2,45,10}*1800, {6,15,10}*1800, {2,15,30}*1800
   10-fold covers : {2,50,10}*2000b, {2,10,10}*2000a, {10,10,10}*2000e, {10,10,10}*2000f, {2,10,10}*2000d
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8,11)( 9,13)(10,12)(14,15)(16,21)(17,20)(18,23)(19,22)
(24,27)(25,26);;
s2 := ( 3, 9)( 4, 6)( 5,16)( 7,18)( 8,12)(10,14)(11,20)(13,24)(15,19)(17,22)
(21,26)(23,25);;
s3 := ( 6, 7)( 9,10)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27);;
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, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(27)!(1,2);
s1 := Sym(27)!( 4, 5)( 6, 7)( 8,11)( 9,13)(10,12)(14,15)(16,21)(17,20)(18,23)
(19,22)(24,27)(25,26);
s2 := Sym(27)!( 3, 9)( 4, 6)( 5,16)( 7,18)( 8,12)(10,14)(11,20)(13,24)(15,19)
(17,22)(21,26)(23,25);
s3 := Sym(27)!( 6, 7)( 9,10)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)
(26,27);
poly := sub<Sym(27)|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, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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