Polytope of Type {15}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {15}*30
Also Known As : 15-gon, {15}. if this polytope has another name.
Group : SmallGroup(30,3)
Rank : 2
Schlafli Type : {15}
Number of vertices, edges, etc : 15, 15
Order of s0s1 : 15
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{15,2} of size 60
{15,4} of size 120
{15,6} of size 180
{15,6} of size 240
{15,4} of size 240
{15,10} of size 300
{15,3} of size 360
{15,6} of size 360
{15,10} of size 360
{15,12} of size 480
{15,8} of size 480
{15,4} of size 480
{15,6} of size 540
{15,5} of size 600
{15,10} of size 600
{15,4} of size 720
{15,6} of size 720
{15,6} of size 720
{15,6} of size 720
{15,6} of size 720
{15,10} of size 720
{15,12} of size 720
{15,6} of size 720
{15,30} of size 900
{15,6} of size 960
{15,8} of size 960
{15,8} of size 960
{15,8} of size 960
{15,10} of size 960
{15,4} of size 960
{15,10} of size 1200
{15,10} of size 1200
{15,20} of size 1200
{15,30} of size 1200
{15,6} of size 1440
{15,6} of size 1440
{15,8} of size 1440
{15,12} of size 1440
{15,12} of size 1440
{15,20} of size 1440
{15,24} of size 1440
{15,12} of size 1440
{15,3} of size 1440
{15,12} of size 1440
{15,15} of size 1440
{15,20} of size 1440
{15,6} of size 1500
{15,10} of size 1500
{15,10} of size 1500
{15,10} of size 1500
{15,10} of size 1500
{15,10} of size 1500
{15,6} of size 1500
{15,10} of size 1500
{15,10} of size 1500
{15,6} of size 1620
{15,18} of size 1620
{15,8} of size 1680
{15,6} of size 1800
{15,10} of size 1800
{15,10} of size 1800
{15,15} of size 1800
{15,15} of size 1800
{15,12} of size 1920
{15,8} of size 1920
{15,20} of size 1920
{15,20} of size 1920
{15,10} of size 1920
{15,8} of size 1920
{15,4} of size 1920
{15,8} of size 1920
{15,4} of size 1920
{15,15} of size 1920
Vertex Figure Of :
{2,15} of size 60
{4,15} of size 120
{6,15} of size 180
{6,15} of size 240
{4,15} of size 240
{10,15} of size 300
{3,15} of size 360
{6,15} of size 360
{10,15} of size 360
{12,15} of size 480
{8,15} of size 480
{4,15} of size 480
{6,15} of size 540
{5,15} of size 600
{10,15} of size 600
{4,15} of size 720
{6,15} of size 720
{6,15} of size 720
{6,15} of size 720
{6,15} of size 720
{10,15} of size 720
{12,15} of size 720
{6,15} of size 720
{30,15} of size 900
{6,15} of size 960
{8,15} of size 960
{8,15} of size 960
{8,15} of size 960
{10,15} of size 960
{4,15} of size 960
{10,15} of size 1200
{10,15} of size 1200
{20,15} of size 1200
{30,15} of size 1200
{6,15} of size 1440
{6,15} of size 1440
{8,15} of size 1440
{12,15} of size 1440
{12,15} of size 1440
{20,15} of size 1440
{24,15} of size 1440
{12,15} of size 1440
{3,15} of size 1440
{12,15} of size 1440
{15,15} of size 1440
{20,15} of size 1440
{6,15} of size 1500
{10,15} of size 1500
{10,15} of size 1500
{10,15} of size 1500
{10,15} of size 1500
{10,15} of size 1500
{6,15} of size 1500
{10,15} of size 1500
{10,15} of size 1500
{6,15} of size 1620
{18,15} of size 1620
{8,15} of size 1680
{6,15} of size 1800
{10,15} of size 1800
{10,15} of size 1800
{15,15} of size 1800
{15,15} of size 1800
{12,15} of size 1920
{8,15} of size 1920
{20,15} of size 1920
{20,15} of size 1920
{10,15} of size 1920
{8,15} of size 1920
{4,15} of size 1920
{8,15} of size 1920
{4,15} of size 1920
{15,15} of size 1920
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {5}*10
5-fold quotients : {3}*6
Covers (Minimal Covers in Boldface) :
2-fold covers : {30}*60
3-fold covers : {45}*90
4-fold covers : {60}*120
5-fold covers : {75}*150
6-fold covers : {90}*180
7-fold covers : {105}*210
8-fold covers : {120}*240
9-fold covers : {135}*270
10-fold covers : {150}*300
11-fold covers : {165}*330
12-fold covers : {180}*360
13-fold covers : {195}*390
14-fold covers : {210}*420
15-fold covers : {225}*450
16-fold covers : {240}*480
17-fold covers : {255}*510
18-fold covers : {270}*540
19-fold covers : {285}*570
20-fold covers : {300}*600
21-fold covers : {315}*630
22-fold covers : {330}*660
23-fold covers : {345}*690
24-fold covers : {360}*720
25-fold covers : {375}*750
26-fold covers : {390}*780
27-fold covers : {405}*810
28-fold covers : {420}*840
29-fold covers : {435}*870
30-fold covers : {450}*900
31-fold covers : {465}*930
32-fold covers : {480}*960
33-fold covers : {495}*990
34-fold covers : {510}*1020
35-fold covers : {525}*1050
36-fold covers : {540}*1080
37-fold covers : {555}*1110
38-fold covers : {570}*1140
39-fold covers : {585}*1170
40-fold covers : {600}*1200
41-fold covers : {615}*1230
42-fold covers : {630}*1260
43-fold covers : {645}*1290
44-fold covers : {660}*1320
45-fold covers : {675}*1350
46-fold covers : {690}*1380
47-fold covers : {705}*1410
48-fold covers : {720}*1440
49-fold covers : {735}*1470
50-fold covers : {750}*1500
51-fold covers : {765}*1530
52-fold covers : {780}*1560
53-fold covers : {795}*1590
54-fold covers : {810}*1620
55-fold covers : {825}*1650
56-fold covers : {840}*1680
57-fold covers : {855}*1710
58-fold covers : {870}*1740
59-fold covers : {885}*1770
60-fold covers : {900}*1800
61-fold covers : {915}*1830
62-fold covers : {930}*1860
63-fold covers : {945}*1890
64-fold covers : {960}*1920
65-fold covers : {975}*1950
66-fold covers : {990}*1980
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);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(15)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13)(14,15);
s1 := Sym(15)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);
poly := sub<Sym(15)|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 >;
References : None.
to this polytope