Polytope of Type {30}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {30}*60
Also Known As : 30-gon, {30}. if this polytope has another name.
Group : SmallGroup(60,12)
Rank : 2
Schlafli Type : {30}
Number of vertices, edges, etc : 30, 30
Order of s0s1 : 30
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{30,2} of size 120
{30,4} of size 240
{30,4} of size 240
{30,4} of size 240
{30,6} of size 360
{30,6} of size 360
{30,6} of size 360
{30,8} of size 480
{30,6} of size 480
{30,4} of size 480
{30,6} of size 540
{30,10} of size 600
{30,10} of size 600
{30,10} of size 600
{30,12} of size 720
{30,12} of size 720
{30,12} of size 720
{30,3} of size 720
{30,6} of size 720
{30,6} of size 720
{30,10} of size 720
{30,10} of size 720
{30,4} of size 720
{30,12} of size 720
{30,14} of size 840
{30,3} of size 900
{30,6} of size 900
{30,15} of size 900
{30,16} of size 960
{30,4} of size 960
{30,8} of size 960
{30,12} of size 960
{30,6} of size 960
{30,12} of size 960
{30,4} of size 960
{30,8} of size 960
{30,8} of size 960
{30,4} of size 960
{30,4} of size 960
{30,18} of size 1080
{30,6} of size 1080
{30,18} of size 1080
{30,6} of size 1080
{30,6} of size 1080
{30,6} of size 1080
{30,20} of size 1200
{30,20} of size 1200
{30,20} of size 1200
{30,4} of size 1200
{30,5} of size 1200
{30,6} of size 1200
{30,10} of size 1200
{30,5} of size 1200
{30,10} of size 1200
{30,10} of size 1200
{30,4} of size 1200
{30,15} of size 1200
{30,20} of size 1200
{30,22} of size 1320
{30,24} of size 1440
{30,24} of size 1440
{30,24} of size 1440
{30,6} of size 1440
{30,6} of size 1440
{30,8} of size 1440
{30,4} of size 1440
{30,6} of size 1440
{30,6} of size 1440
{30,6} of size 1440
{30,6} of size 1440
{30,10} of size 1440
{30,6} of size 1440
{30,12} of size 1440
{30,12} of size 1440
{30,6} of size 1440
{30,3} of size 1500
{30,10} of size 1500
{30,10} of size 1500
{30,10} of size 1500
{30,10} of size 1500
{30,10} of size 1500
{30,10} of size 1500
{30,26} of size 1560
{30,18} of size 1620
{30,6} of size 1620
{30,6} of size 1620
{30,18} of size 1620
{30,18} of size 1620
{30,28} of size 1680
{30,28} of size 1680
{30,6} of size 1800
{30,6} of size 1800
{30,6} of size 1800
{30,6} of size 1800
{30,4} of size 1800
{30,30} of size 1800
{30,30} of size 1800
{30,30} of size 1800
{30,30} of size 1800
{30,30} of size 1800
{30,30} of size 1800
{30,30} of size 1800
{30,30} of size 1800
{30,30} of size 1800
{30,32} of size 1920
{30,8} of size 1920
{30,8} of size 1920
{30,8} of size 1920
{30,6} of size 1920
{30,6} of size 1920
{30,6} of size 1920
{30,24} of size 1920
{30,12} of size 1920
{30,24} of size 1920
{30,4} of size 1920
{30,8} of size 1920
{30,8} of size 1920
{30,8} of size 1920
{30,8} of size 1920
{30,4} of size 1920
{30,10} of size 1920
{30,8} of size 1920
{30,8} of size 1920
{30,8} of size 1920
{30,8} of size 1920
{30,4} of size 1920
{30,10} of size 1920
{30,4} of size 1920
Vertex Figure Of :
{2,30} of size 120
{4,30} of size 240
{4,30} of size 240
{4,30} of size 240
{6,30} of size 360
{6,30} of size 360
{6,30} of size 360
{8,30} of size 480
{6,30} of size 480
{4,30} of size 480
{6,30} of size 540
{10,30} of size 600
{10,30} of size 600
{10,30} of size 600
{12,30} of size 720
{12,30} of size 720
{12,30} of size 720
{3,30} of size 720
{6,30} of size 720
{6,30} of size 720
{10,30} of size 720
{10,30} of size 720
{4,30} of size 720
{12,30} of size 720
{14,30} of size 840
{3,30} of size 900
{6,30} of size 900
{15,30} of size 900
{16,30} of size 960
{4,30} of size 960
{8,30} of size 960
{12,30} of size 960
{6,30} of size 960
{12,30} of size 960
{4,30} of size 960
{8,30} of size 960
{8,30} of size 960
{4,30} of size 960
{4,30} of size 960
{18,30} of size 1080
{6,30} of size 1080
{18,30} of size 1080
{6,30} of size 1080
{6,30} of size 1080
{6,30} of size 1080
{20,30} of size 1200
{20,30} of size 1200
{20,30} of size 1200
{4,30} of size 1200
{5,30} of size 1200
{6,30} of size 1200
{10,30} of size 1200
{5,30} of size 1200
{10,30} of size 1200
{10,30} of size 1200
{4,30} of size 1200
{15,30} of size 1200
{20,30} of size 1200
{22,30} of size 1320
{24,30} of size 1440
{24,30} of size 1440
{24,30} of size 1440
{6,30} of size 1440
{6,30} of size 1440
{8,30} of size 1440
{4,30} of size 1440
{6,30} of size 1440
{6,30} of size 1440
{6,30} of size 1440
{6,30} of size 1440
{10,30} of size 1440
{6,30} of size 1440
{12,30} of size 1440
{12,30} of size 1440
{6,30} of size 1440
{3,30} of size 1500
{10,30} of size 1500
{10,30} of size 1500
{10,30} of size 1500
{10,30} of size 1500
{10,30} of size 1500
{10,30} of size 1500
{26,30} of size 1560
{18,30} of size 1620
{6,30} of size 1620
{6,30} of size 1620
{18,30} of size 1620
{18,30} of size 1620
{28,30} of size 1680
{28,30} of size 1680
{6,30} of size 1800
{6,30} of size 1800
{6,30} of size 1800
{6,30} of size 1800
{4,30} of size 1800
{30,30} of size 1800
{30,30} of size 1800
{30,30} of size 1800
{30,30} of size 1800
{30,30} of size 1800
{30,30} of size 1800
{30,30} of size 1800
{30,30} of size 1800
{30,30} of size 1800
{32,30} of size 1920
{8,30} of size 1920
{8,30} of size 1920
{8,30} of size 1920
{6,30} of size 1920
{6,30} of size 1920
{6,30} of size 1920
{24,30} of size 1920
{12,30} of size 1920
{24,30} of size 1920
{4,30} of size 1920
{8,30} of size 1920
{8,30} of size 1920
{8,30} of size 1920
{8,30} of size 1920
{4,30} of size 1920
{10,30} of size 1920
{8,30} of size 1920
{8,30} of size 1920
{8,30} of size 1920
{8,30} of size 1920
{4,30} of size 1920
{10,30} of size 1920
{4,30} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {15}*30
3-fold quotients : {10}*20
5-fold quotients : {6}*12
6-fold quotients : {5}*10
10-fold quotients : {3}*6
15-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {60}*120
3-fold covers : {90}*180
4-fold covers : {120}*240
5-fold covers : {150}*300
6-fold covers : {180}*360
7-fold covers : {210}*420
8-fold covers : {240}*480
9-fold covers : {270}*540
10-fold covers : {300}*600
11-fold covers : {330}*660
12-fold covers : {360}*720
13-fold covers : {390}*780
14-fold covers : {420}*840
15-fold covers : {450}*900
16-fold covers : {480}*960
17-fold covers : {510}*1020
18-fold covers : {540}*1080
19-fold covers : {570}*1140
20-fold covers : {600}*1200
21-fold covers : {630}*1260
22-fold covers : {660}*1320
23-fold covers : {690}*1380
24-fold covers : {720}*1440
25-fold covers : {750}*1500
26-fold covers : {780}*1560
27-fold covers : {810}*1620
28-fold covers : {840}*1680
29-fold covers : {870}*1740
30-fold covers : {900}*1800
31-fold covers : {930}*1860
32-fold covers : {960}*1920
33-fold covers : {990}*1980
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,14)(12,13)(15,16)(17,20)(18,19)(21,22)
(23,26)(24,25)(27,30)(28,29);;
s1 := ( 1,17)( 2,11)( 3, 9)( 4,19)( 5, 7)( 6,27)( 8,13)(10,23)(12,21)(14,29)
(15,18)(16,28)(20,25)(22,24)(26,30);;
poly := Group([s0,s1]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;; s1 := F.2;;
rels := [ s0*s0, s1*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*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*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(30)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,14)(12,13)(15,16)(17,20)(18,19)
(21,22)(23,26)(24,25)(27,30)(28,29);
s1 := Sym(30)!( 1,17)( 2,11)( 3, 9)( 4,19)( 5, 7)( 6,27)( 8,13)(10,23)(12,21)
(14,29)(15,18)(16,28)(20,25)(22,24)(26,30);
poly := sub<Sym(30)|s0,s1>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*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*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*s0*s1 >;
References : None.
to this polytope