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Polytope of Type {3,2,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,2,2,5}*120
if this polytope has a name.
Group : SmallGroup(120,42)
Rank : 5
Schlafli Type : {3,2,2,5}
Number of vertices, edges, etc : 3, 3, 2, 5, 5
Order of s0s1s2s3s4 : 30
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,2,2,5,2} of size 240
   {3,2,2,5,3} of size 720
   {3,2,2,5,5} of size 720
   {3,2,2,5,10} of size 1200
   {3,2,2,5,4} of size 1440
   {3,2,2,5,6} of size 1440
   {3,2,2,5,3} of size 1440
   {3,2,2,5,5} of size 1440
   {3,2,2,5,6} of size 1440
   {3,2,2,5,6} of size 1440
   {3,2,2,5,10} of size 1440
   {3,2,2,5,10} of size 1440
   {3,2,2,5,4} of size 1920
   {3,2,2,5,5} of size 1920
Vertex Figure Of :
   {2,3,2,2,5} of size 240
   {3,3,2,2,5} of size 480
   {4,3,2,2,5} of size 480
   {6,3,2,2,5} of size 720
   {4,3,2,2,5} of size 960
   {6,3,2,2,5} of size 960
   {5,3,2,2,5} of size 1200
   {8,3,2,2,5} of size 1920
   {12,3,2,2,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,2,2,10}*240, {6,2,2,5}*240
   3-fold covers : {9,2,2,5}*360, {3,6,2,5}*360, {3,2,2,15}*360
   4-fold covers : {12,2,2,5}*480, {3,2,2,20}*480, {3,2,4,10}*480, {6,4,2,5}*480a, {3,4,2,5}*480, {6,2,2,10}*480
   5-fold covers : {3,2,2,25}*600, {3,2,10,5}*600, {15,2,2,5}*600
   6-fold covers : {9,2,2,10}*720, {18,2,2,5}*720, {3,2,6,10}*720, {3,6,2,10}*720, {6,6,2,5}*720a, {6,6,2,5}*720c, {3,2,2,30}*720, {6,2,2,15}*720
   7-fold covers : {21,2,2,5}*840, {3,2,2,35}*840
   8-fold covers : {12,4,2,5}*960a, {3,2,4,20}*960, {24,2,2,5}*960, {3,2,2,40}*960, {3,2,8,10}*960, {6,8,2,5}*960, {3,8,2,5}*960, {12,2,2,10}*960, {6,2,2,20}*960, {6,2,4,10}*960, {6,4,2,10}*960a, {3,4,2,10}*960, {6,4,2,5}*960
   9-fold covers : {27,2,2,5}*1080, {9,6,2,5}*1080, {3,6,2,5}*1080, {3,2,2,45}*1080, {9,2,2,15}*1080, {3,2,6,15}*1080, {3,6,2,15}*1080
   10-fold covers : {3,2,2,50}*1200, {6,2,2,25}*1200, {3,2,10,10}*1200a, {3,2,10,10}*1200b, {6,2,10,5}*1200, {6,10,2,5}*1200, {15,2,2,10}*1200, {30,2,2,5}*1200
   11-fold covers : {33,2,2,5}*1320, {3,2,2,55}*1320
   12-fold covers : {36,2,2,5}*1440, {9,2,2,20}*1440, {9,2,4,10}*1440, {18,4,2,5}*1440a, {9,4,2,5}*1440, {18,2,2,10}*1440, {3,2,12,10}*1440, {6,12,2,5}*1440a, {12,6,2,5}*1440a, {12,6,2,5}*1440b, {3,2,6,20}*1440a, {3,6,2,20}*1440, {3,6,4,10}*1440, {6,12,2,5}*1440c, {12,2,2,15}*1440, {3,2,2,60}*1440, {3,2,4,30}*1440a, {6,4,2,15}*1440a, {3,2,6,15}*1440, {3,6,2,5}*1440, {3,12,2,5}*1440, {3,2,4,15}*1440, {3,4,2,15}*1440, {6,2,6,10}*1440, {6,6,2,10}*1440a, {6,6,2,10}*1440c, {6,2,2,30}*1440
   13-fold covers : {39,2,2,5}*1560, {3,2,2,65}*1560
   14-fold covers : {3,2,14,10}*1680, {6,14,2,5}*1680, {21,2,2,10}*1680, {42,2,2,5}*1680, {3,2,2,70}*1680, {6,2,2,35}*1680
   15-fold covers : {9,2,2,25}*1800, {3,6,2,25}*1800, {3,2,2,75}*1800, {9,2,10,5}*1800, {45,2,2,5}*1800, {3,2,10,15}*1800, {15,6,2,5}*1800, {3,6,10,5}*1800, {15,2,2,15}*1800
   16-fold covers : {12,8,2,5}*1920a, {3,2,8,20}*1920a, {24,4,2,5}*1920a, {3,2,4,40}*1920a, {12,8,2,5}*1920b, {3,2,8,20}*1920b, {24,4,2,5}*1920b, {3,2,4,40}*1920b, {12,4,2,5}*1920a, {3,2,4,20}*1920, {3,2,16,10}*1920, {6,16,2,5}*1920, {48,2,2,5}*1920, {3,2,2,80}*1920, {6,4,4,10}*1920, {12,4,2,10}*1920a, {6,2,4,20}*1920, {12,2,4,10}*1920, {6,4,2,20}*1920a, {12,2,2,20}*1920, {6,2,8,10}*1920, {6,8,2,10}*1920, {24,2,2,10}*1920, {6,2,2,40}*1920, {3,8,2,5}*1920, {12,4,2,5}*1920b, {3,4,2,20}*1920, {3,4,4,10}*1920b, {6,4,2,5}*1920b, {12,4,2,5}*1920c, {3,8,2,10}*1920, {6,8,2,5}*1920b, {6,8,2,5}*1920c, {3,2,4,5}*1920, {6,4,2,10}*1920
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2);;
s2 := (4,5);;
s3 := ( 7, 8)( 9,10);;
s4 := (6,7)(8,9);;
poly := Group([s0,s1,s2,s3,s4]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(10)!(2,3);
s1 := Sym(10)!(1,2);
s2 := Sym(10)!(4,5);
s3 := Sym(10)!( 7, 8)( 9,10);
s4 := Sym(10)!(6,7)(8,9);
poly := sub<Sym(10)|s0,s1,s2,s3,s4>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

to this polytope