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Polytope of Type {15,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15,2,2}*120
if this polytope has a name.
Group : SmallGroup(120,46)
Rank : 4
Schlafli Type : {15,2,2}
Number of vertices, edges, etc : 15, 15, 2, 2
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {15,2,2,2} of size 240
   {15,2,2,3} of size 360
   {15,2,2,4} of size 480
   {15,2,2,5} of size 600
   {15,2,2,6} of size 720
   {15,2,2,7} of size 840
   {15,2,2,8} of size 960
   {15,2,2,9} of size 1080
   {15,2,2,10} of size 1200
   {15,2,2,11} of size 1320
   {15,2,2,12} of size 1440
   {15,2,2,13} of size 1560
   {15,2,2,14} of size 1680
   {15,2,2,15} of size 1800
   {15,2,2,16} of size 1920
Vertex Figure Of :
   {2,15,2,2} of size 240
   {4,15,2,2} of size 480
   {6,15,2,2} of size 720
   {6,15,2,2} of size 960
   {4,15,2,2} of size 960
   {10,15,2,2} of size 1200
   {3,15,2,2} of size 1440
   {6,15,2,2} of size 1440
   {10,15,2,2} of size 1440
   {12,15,2,2} of size 1920
   {8,15,2,2} of size 1920
   {4,15,2,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {5,2,2}*40
   5-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {15,2,4}*240, {30,2,2}*240
   3-fold covers : {45,2,2}*360, {15,2,6}*360, {15,6,2}*360
   4-fold covers : {15,2,8}*480, {60,2,2}*480, {30,2,4}*480, {30,4,2}*480a, {15,4,2}*480
   5-fold covers : {75,2,2}*600, {15,2,10}*600, {15,10,2}*600
   6-fold covers : {45,2,4}*720, {90,2,2}*720, {15,2,12}*720, {15,6,4}*720, {30,2,6}*720, {30,6,2}*720b, {30,6,2}*720c
   7-fold covers : {15,2,14}*840, {105,2,2}*840
   8-fold covers : {15,2,16}*960, {60,4,2}*960a, {60,2,4}*960, {30,4,4}*960, {120,2,2}*960, {30,2,8}*960, {30,8,2}*960, {15,4,4}*960b, {15,8,2}*960, {30,4,2}*960
   9-fold covers : {135,2,2}*1080, {45,2,6}*1080, {45,6,2}*1080, {15,2,18}*1080, {15,6,6}*1080a, {15,6,2}*1080, {15,6,6}*1080b
   10-fold covers : {75,2,4}*1200, {150,2,2}*1200, {15,2,20}*1200, {15,10,4}*1200, {30,2,10}*1200, {30,10,2}*1200b, {30,10,2}*1200c
   11-fold covers : {15,2,22}*1320, {165,2,2}*1320
   12-fold covers : {45,2,8}*1440, {180,2,2}*1440, {90,2,4}*1440, {90,4,2}*1440a, {15,2,24}*1440, {15,6,8}*1440, {45,4,2}*1440, {30,2,12}*1440, {30,12,2}*1440b, {60,2,6}*1440, {60,6,2}*1440b, {60,6,2}*1440c, {30,4,6}*1440, {30,6,4}*1440b, {30,6,4}*1440c, {30,12,2}*1440c, {15,4,6}*1440, {15,12,2}*1440, {15,6,2}*1440e
   13-fold covers : {15,2,26}*1560, {195,2,2}*1560
   14-fold covers : {15,2,28}*1680, {105,2,4}*1680, {30,2,14}*1680, {30,14,2}*1680, {210,2,2}*1680
   15-fold covers : {225,2,2}*1800, {75,2,6}*1800, {75,6,2}*1800, {45,2,10}*1800, {45,10,2}*1800, {15,6,10}*1800, {15,10,6}*1800, {15,2,30}*1800, {15,30,2}*1800
   16-fold covers : {15,2,32}*1920, {60,4,4}*1920, {30,4,8}*1920a, {30,8,4}*1920a, {60,8,2}*1920a, {120,4,2}*1920a, {30,4,8}*1920b, {30,8,4}*1920b, {60,8,2}*1920b, {120,4,2}*1920b, {30,4,4}*1920a, {60,4,2}*1920a, {60,2,8}*1920, {120,2,4}*1920, {30,2,16}*1920, {30,16,2}*1920, {240,2,2}*1920, {15,4,4}*1920b, {15,8,2}*1920a, {15,8,4}*1920, {15,4,8}*1920, {60,4,2}*1920b, {30,4,4}*1920d, {30,4,2}*1920b, {60,4,2}*1920c, {30,8,2}*1920b, {30,8,2}*1920c, {15,4,2}*1920
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);;
s2 := (16,17);;
s3 := (18,19);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(19)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15);
s1 := Sym(19)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);
s2 := Sym(19)!(16,17);
s3 := Sym(19)!(18,19);
poly := sub<Sym(19)|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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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