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