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Polytope of Type {2,5,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,5,5}*120
if this polytope has a name.
Group : SmallGroup(120,35)
Rank : 4
Schlafli Type : {2,5,5}
Number of vertices, edges, etc : 2, 6, 15, 6
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,5,5,2} of size 240
Vertex Figure Of :
   {2,2,5,5} of size 240
   {3,2,5,5} of size 360
   {4,2,5,5} of size 480
   {5,2,5,5} of size 600
   {6,2,5,5} of size 720
   {7,2,5,5} of size 840
   {8,2,5,5} of size 960
   {9,2,5,5} of size 1080
   {10,2,5,5} of size 1200
   {11,2,5,5} of size 1320
   {12,2,5,5} of size 1440
   {13,2,5,5} of size 1560
   {14,2,5,5} of size 1680
   {15,2,5,5} of size 1800
   {16,2,5,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,5,5}*240, {2,5,10}*240a, {2,5,10}*240b, {2,10,5}*240a, {2,10,5}*240b
   4-fold covers : {4,10,5}*480, {2,5,10}*480, {2,10,5}*480, {2,10,10}*480a, {2,10,10}*480b, {2,10,10}*480c, {2,10,10}*480d
   6-fold covers : {6,10,5}*720, {2,10,15}*720, {2,15,10}*720
   8-fold covers : {8,10,5}*960, {4,10,5}*960, {4,10,10}*960a, {4,10,10}*960b, {2,10,20}*960a, {2,10,20}*960b, {2,20,10}*960a, {2,20,10}*960b, {2,5,20}*960, {2,20,5}*960, {2,10,10}*960
   10-fold covers : {2,5,5}*1200, {2,5,10}*1200, {2,10,5}*1200, {10,10,5}*1200
   12-fold covers : {12,10,5}*1440, {6,10,5}*1440, {6,10,10}*1440a, {6,10,10}*1440b, {2,10,15}*1440, {2,10,30}*1440a, {2,10,30}*1440b, {2,15,10}*1440, {2,30,10}*1440a, {2,30,10}*1440b
   14-fold covers : {2,10,35}*1680, {2,35,10}*1680, {14,10,5}*1680
   16-fold covers : {16,10,5}*1920, {4,20,10}*1920a, {4,20,10}*1920b, {8,10,5}*1920, {8,10,10}*1920a, {8,10,10}*1920b, {2,10,40}*1920a, {2,10,40}*1920b, {2,40,10}*1920a, {2,40,10}*1920b, {4,10,10}*1920, {2,10,20}*1920a, {2,20,10}*1920a, {4,20,5}*1920, {2,10,20}*1920b, {2,20,10}*1920b, {2,10,10}*1920, {4,5,5}*1920, {2,5,5}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (4,5)(6,7);;
s2 := (3,4)(5,6);;
s3 := (4,6)(5,7);;
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*s1*s2*s3*s1*s2*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(7)!(1,2);
s1 := Sym(7)!(4,5)(6,7);
s2 := Sym(7)!(3,4)(5,6);
s3 := Sym(7)!(4,6)(5,7);
poly := sub<Sym(7)|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*s1*s2*s3*s1*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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