Polytope of Type {2,5}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,5}*20
if this polytope has a name.
Group : SmallGroup(20,4)
Rank : 3
Schlafli Type : {2,5}
Number of vertices, edges, etc : 2, 5, 5
Order of s0s1s2 : 10
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,5,2} of size 40
{2,5,3} of size 120
{2,5,5} of size 120
{2,5,10} of size 200
{2,5,4} of size 240
{2,5,6} of size 240
{2,5,3} of size 240
{2,5,5} of size 240
{2,5,6} of size 240
{2,5,6} of size 240
{2,5,10} of size 240
{2,5,10} of size 240
{2,5,4} of size 320
{2,5,5} of size 320
{2,5,4} of size 480
{2,5,6} of size 480
{2,5,6} of size 480
{2,5,10} of size 480
{2,5,5} of size 640
{2,5,8} of size 640
{2,5,8} of size 640
{2,5,10} of size 640
{2,5,4} of size 640
{2,5,10} of size 640
{2,5,6} of size 960
{2,5,8} of size 960
{2,5,12} of size 960
{2,5,20} of size 960
{2,5,10} of size 1000
{2,5,5} of size 1200
{2,5,6} of size 1200
{2,5,10} of size 1200
{2,5,15} of size 1200
{2,5,8} of size 1280
{2,5,10} of size 1280
{2,5,4} of size 1280
{2,5,8} of size 1280
{2,5,20} of size 1280
{2,5,20} of size 1280
{2,5,5} of size 1320
{2,5,6} of size 1320
{2,5,6} of size 1440
{2,5,4} of size 1440
{2,5,5} of size 1440
{2,5,8} of size 1440
{2,5,8} of size 1440
{2,5,10} of size 1440
{2,5,5} of size 1920
{2,5,6} of size 1920
Vertex Figure Of :
{2,2,5} of size 40
{3,2,5} of size 60
{4,2,5} of size 80
{5,2,5} of size 100
{6,2,5} of size 120
{7,2,5} of size 140
{8,2,5} of size 160
{9,2,5} of size 180
{10,2,5} of size 200
{11,2,5} of size 220
{12,2,5} of size 240
{13,2,5} of size 260
{14,2,5} of size 280
{15,2,5} of size 300
{16,2,5} of size 320
{17,2,5} of size 340
{18,2,5} of size 360
{19,2,5} of size 380
{20,2,5} of size 400
{21,2,5} of size 420
{22,2,5} of size 440
{23,2,5} of size 460
{24,2,5} of size 480
{25,2,5} of size 500
{26,2,5} of size 520
{27,2,5} of size 540
{28,2,5} of size 560
{29,2,5} of size 580
{30,2,5} of size 600
{31,2,5} of size 620
{32,2,5} of size 640
{33,2,5} of size 660
{34,2,5} of size 680
{35,2,5} of size 700
{36,2,5} of size 720
{37,2,5} of size 740
{38,2,5} of size 760
{39,2,5} of size 780
{40,2,5} of size 800
{41,2,5} of size 820
{42,2,5} of size 840
{43,2,5} of size 860
{44,2,5} of size 880
{45,2,5} of size 900
{46,2,5} of size 920
{47,2,5} of size 940
{48,2,5} of size 960
{49,2,5} of size 980
{50,2,5} of size 1000
{51,2,5} of size 1020
{52,2,5} of size 1040
{53,2,5} of size 1060
{54,2,5} of size 1080
{55,2,5} of size 1100
{56,2,5} of size 1120
{57,2,5} of size 1140
{58,2,5} of size 1160
{59,2,5} of size 1180
{60,2,5} of size 1200
{61,2,5} of size 1220
{62,2,5} of size 1240
{63,2,5} of size 1260
{64,2,5} of size 1280
{65,2,5} of size 1300
{66,2,5} of size 1320
{67,2,5} of size 1340
{68,2,5} of size 1360
{69,2,5} of size 1380
{70,2,5} of size 1400
{71,2,5} of size 1420
{72,2,5} of size 1440
{73,2,5} of size 1460
{74,2,5} of size 1480
{75,2,5} of size 1500
{76,2,5} of size 1520
{77,2,5} of size 1540
{78,2,5} of size 1560
{79,2,5} of size 1580
{80,2,5} of size 1600
{81,2,5} of size 1620
{82,2,5} of size 1640
{83,2,5} of size 1660
{84,2,5} of size 1680
{85,2,5} of size 1700
{86,2,5} of size 1720
{87,2,5} of size 1740
{88,2,5} of size 1760
{89,2,5} of size 1780
{90,2,5} of size 1800
{91,2,5} of size 1820
{92,2,5} of size 1840
{93,2,5} of size 1860
{94,2,5} of size 1880
{95,2,5} of size 1900
{96,2,5} of size 1920
{97,2,5} of size 1940
{98,2,5} of size 1960
{99,2,5} of size 1980
{100,2,5} of size 2000
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,10}*40
3-fold covers : {2,15}*60
4-fold covers : {2,20}*80, {4,10}*80
5-fold covers : {2,25}*100, {10,5}*100
6-fold covers : {6,10}*120, {2,30}*120
7-fold covers : {2,35}*140
8-fold covers : {4,20}*160, {2,40}*160, {8,10}*160
9-fold covers : {2,45}*180, {6,15}*180
10-fold covers : {2,50}*200, {10,10}*200a, {10,10}*200b
11-fold covers : {2,55}*220
12-fold covers : {12,10}*240, {6,20}*240a, {2,60}*240, {4,30}*240a, {6,15}*240, {4,15}*240
13-fold covers : {2,65}*260
14-fold covers : {14,10}*280, {2,70}*280
15-fold covers : {2,75}*300, {10,15}*300
16-fold covers : {4,40}*320a, {4,20}*320, {4,40}*320b, {8,20}*320a, {8,20}*320b, {2,80}*320, {16,10}*320, {4,5}*320
17-fold covers : {2,85}*340
18-fold covers : {18,10}*360, {2,90}*360, {6,30}*360a, {6,30}*360b, {6,30}*360c
19-fold covers : {2,95}*380
20-fold covers : {2,100}*400, {4,50}*400, {10,20}*400a, {10,20}*400b, {20,10}*400a, {20,10}*400c
21-fold covers : {2,105}*420
22-fold covers : {22,10}*440, {2,110}*440
23-fold covers : {2,115}*460
24-fold covers : {24,10}*480, {6,40}*480, {12,20}*480, {4,60}*480a, {2,120}*480, {8,30}*480, {12,15}*480, {8,15}*480, {6,20}*480c, {6,30}*480, {4,30}*480
25-fold covers : {2,125}*500, {10,25}*500, {10,5}*500
26-fold covers : {26,10}*520, {2,130}*520
27-fold covers : {2,135}*540, {6,45}*540, {6,15}*540
28-fold covers : {14,20}*560, {28,10}*560, {2,140}*560, {4,70}*560
29-fold covers : {2,145}*580
30-fold covers : {6,50}*600, {2,150}*600, {30,10}*600a, {10,30}*600b, {10,30}*600c, {30,10}*600b
31-fold covers : {2,155}*620
32-fold covers : {4,40}*640a, {8,40}*640a, {8,40}*640b, {8,20}*640a, {8,40}*640c, {8,40}*640d, {4,80}*640a, {4,80}*640b, {4,20}*640a, {4,40}*640b, {8,20}*640b, {16,20}*640a, {16,20}*640b, {2,160}*640, {32,10}*640, {8,5}*640a, {4,5}*640, {4,10}*640a, {8,5}*640b, {4,10}*640b
33-fold covers : {2,165}*660
34-fold covers : {34,10}*680, {2,170}*680
35-fold covers : {2,175}*700, {10,35}*700
36-fold covers : {36,10}*720, {18,20}*720a, {2,180}*720, {4,90}*720a, {4,45}*720, {6,60}*720a, {12,30}*720a, {12,30}*720b, {6,60}*720b, {6,60}*720c, {12,30}*720c, {4,20}*720, {4,30}*720, {12,15}*720, {6,15}*720e, {6,20}*720
37-fold covers : {2,185}*740
38-fold covers : {38,10}*760, {2,190}*760
39-fold covers : {2,195}*780
40-fold covers : {4,100}*800, {2,200}*800, {8,50}*800, {10,40}*800a, {10,40}*800b, {40,10}*800a, {20,20}*800a, {20,20}*800b, {40,10}*800c
41-fold covers : {2,205}*820
42-fold covers : {14,30}*840, {42,10}*840, {6,70}*840, {2,210}*840
43-fold covers : {2,215}*860
44-fold covers : {22,20}*880, {44,10}*880, {2,220}*880, {4,110}*880
45-fold covers : {2,225}*900, {6,75}*900, {10,45}*900, {30,15}*900
46-fold covers : {46,10}*920, {2,230}*920
47-fold covers : {2,235}*940
48-fold covers : {48,10}*960, {6,80}*960, {12,20}*960a, {24,20}*960a, {12,40}*960a, {24,20}*960b, {12,40}*960b, {4,120}*960a, {4,60}*960a, {4,120}*960b, {8,60}*960a, {8,60}*960b, {2,240}*960, {16,30}*960, {6,15}*960, {8,15}*960a, {12,20}*960b, {6,20}*960e, {6,60}*960a, {12,30}*960a, {6,30}*960, {6,40}*960d, {6,40}*960e, {6,60}*960b, {12,20}*960c, {12,30}*960b, {4,60}*960b, {4,30}*960b, {4,60}*960c, {8,30}*960b, {8,30}*960c, {4,15}*960
49-fold covers : {2,245}*980, {14,35}*980
50-fold covers : {2,250}*1000, {10,50}*1000a, {10,50}*1000b, {50,10}*1000a, {10,10}*1000b, {10,10}*1000c, {10,10}*1000d
51-fold covers : {2,255}*1020
52-fold covers : {26,20}*1040, {52,10}*1040, {2,260}*1040, {4,130}*1040
53-fold covers : {2,265}*1060
54-fold covers : {54,10}*1080, {2,270}*1080, {18,30}*1080a, {6,30}*1080a, {6,90}*1080a, {6,90}*1080b, {18,30}*1080b, {6,30}*1080b, {6,30}*1080c, {6,30}*1080d
55-fold covers : {2,275}*1100, {10,55}*1100
56-fold covers : {14,40}*1120, {56,10}*1120, {28,20}*1120, {4,140}*1120, {2,280}*1120, {8,70}*1120
57-fold covers : {2,285}*1140
58-fold covers : {58,10}*1160, {2,290}*1160
59-fold covers : {2,295}*1180
60-fold covers : {12,50}*1200, {6,100}*1200a, {2,300}*1200, {4,150}*1200a, {6,75}*1200, {4,75}*1200, {30,20}*1200a, {60,10}*1200a, {20,30}*1200b, {30,20}*1200b, {10,60}*1200b, {10,60}*1200c, {60,10}*1200b, {20,30}*1200c, {4,5}*1200, {6,5}*1200a, {6,5}*1200b, {10,5}*1200a, {10,15}*1200a, {20,15}*1200, {30,15}*1200
61-fold covers : {2,305}*1220
62-fold covers : {62,10}*1240, {2,310}*1240
63-fold covers : {2,315}*1260, {6,105}*1260
64-fold covers : {8,40}*1280a, {8,20}*1280a, {8,40}*1280b, {4,40}*1280a, {8,40}*1280c, {8,40}*1280d, {16,20}*1280a, {4,80}*1280a, {16,20}*1280b, {4,80}*1280b, {8,80}*1280a, {16,40}*1280a, {8,80}*1280b, {16,40}*1280b, {16,40}*1280c, {8,80}*1280c, {8,80}*1280d, {16,40}*1280d, {16,40}*1280e, {8,80}*1280e, {8,80}*1280f, {16,40}*1280f, {32,20}*1280a, {4,160}*1280a, {32,20}*1280b, {4,160}*1280b, {4,20}*1280a, {4,40}*1280b, {8,20}*1280b, {8,20}*1280c, {8,40}*1280e, {4,40}*1280c, {4,40}*1280d, {8,20}*1280d, {8,40}*1280f, {8,40}*1280g, {8,40}*1280h, {64,10}*1280, {2,320}*1280, {8,5}*1280, {8,10}*1280a, {8,10}*1280b, {4,10}*1280a, {4,20}*1280b, {4,20}*1280c, {8,10}*1280c, {4,10}*1280b, {4,20}*1280d, {8,10}*1280d, {4,20}*1280e, {4,10}*1280c, {8,10}*1280e, {8,10}*1280f
65-fold covers : {2,325}*1300, {10,65}*1300
66-fold covers : {22,30}*1320, {66,10}*1320, {6,110}*1320, {2,330}*1320
67-fold covers : {2,335}*1340
68-fold covers : {34,20}*1360, {68,10}*1360, {2,340}*1360, {4,170}*1360
69-fold covers : {2,345}*1380
70-fold covers : {14,50}*1400, {2,350}*1400, {70,10}*1400a, {10,70}*1400b, {10,70}*1400c, {70,10}*1400b
71-fold covers : {2,355}*1420
72-fold covers : {72,10}*1440, {18,40}*1440, {36,20}*1440, {4,180}*1440a, {2,360}*1440, {8,90}*1440, {8,45}*1440, {6,120}*1440a, {24,30}*1440a, {12,60}*1440a, {24,30}*1440b, {6,120}*1440b, {6,120}*1440c, {12,60}*1440b, {12,60}*1440c, {24,30}*1440c, {18,20}*1440, {4,90}*1440, {4,20}*1440, {4,60}*1440, {8,30}*1440, {24,15}*1440, {12,15}*1440c, {6,40}*1440, {12,20}*1440, {6,30}*1440g, {6,60}*1440c, {12,30}*1440a, {12,30}*1440b, {6,30}*1440h, {6,60}*1440d
73-fold covers : {2,365}*1460
74-fold covers : {74,10}*1480, {2,370}*1480
75-fold covers : {2,375}*1500, {10,75}*1500, {10,15}*1500e, {6,15}*1500b, {10,15}*1500g
76-fold covers : {38,20}*1520, {76,10}*1520, {2,380}*1520, {4,190}*1520
77-fold covers : {2,385}*1540
78-fold covers : {26,30}*1560, {78,10}*1560, {6,130}*1560, {2,390}*1560
79-fold covers : {2,395}*1580
80-fold covers : {4,200}*1600a, {4,100}*1600, {4,200}*1600b, {8,100}*1600a, {8,100}*1600b, {2,400}*1600, {16,50}*1600, {10,80}*1600a, {10,80}*1600b, {80,10}*1600a, {40,20}*1600a, {20,20}*1600a, {20,20}*1600b, {40,20}*1600b, {20,40}*1600c, {20,40}*1600d, {40,20}*1600c, {20,40}*1600e, {20,40}*1600f, {40,20}*1600e, {80,10}*1600c, {4,25}*1600, {10,5}*1600, {20,5}*1600
81-fold covers : {2,405}*1620, {18,45}*1620, {6,45}*1620a, {6,135}*1620, {6,45}*1620b, {6,45}*1620c, {6,45}*1620d, {6,15}*1620, {18,15}*1620, {6,5}*1620
82-fold covers : {82,10}*1640, {2,410}*1640
83-fold covers : {2,415}*1660
84-fold covers : {14,60}*1680, {28,30}*1680a, {42,20}*1680a, {84,10}*1680, {12,70}*1680, {6,140}*1680a, {2,420}*1680, {4,210}*1680a, {6,105}*1680, {4,105}*1680
85-fold covers : {2,425}*1700, {10,85}*1700
86-fold covers : {86,10}*1720, {2,430}*1720
87-fold covers : {2,435}*1740
88-fold covers : {22,40}*1760, {88,10}*1760, {44,20}*1760, {4,220}*1760, {2,440}*1760, {8,110}*1760
89-fold covers : {2,445}*1780
90-fold covers : {18,50}*1800, {2,450}*1800, {6,150}*1800a, {6,150}*1800b, {6,150}*1800c, {90,10}*1800a, {10,90}*1800b, {10,90}*1800c, {90,10}*1800b, {30,30}*1800a, {30,30}*1800b, {30,30}*1800c, {30,30}*1800d, {30,30}*1800g, {30,30}*1800h
91-fold covers : {2,455}*1820
92-fold covers : {46,20}*1840, {92,10}*1840, {2,460}*1840, {4,230}*1840
93-fold covers : {2,465}*1860
94-fold covers : {94,10}*1880, {2,470}*1880
95-fold covers : {2,475}*1900, {10,95}*1900
96-fold covers : {8,60}*1920a, {4,120}*1920a, {12,40}*1920a, {24,20}*1920a, {8,120}*1920a, {8,120}*1920b, {8,120}*1920c, {24,40}*1920a, {24,40}*1920b, {24,40}*1920c, {8,120}*1920d, {24,40}*1920d, {16,60}*1920a, {4,240}*1920a, {12,80}*1920a, {48,20}*1920a, {16,60}*1920b, {4,240}*1920b, {12,80}*1920b, {48,20}*1920b, {4,60}*1920a, {4,120}*1920b, {8,60}*1920b, {12,40}*1920b, {24,20}*1920b, {12,20}*1920a, {32,30}*1920, {2,480}*1920, {96,10}*1920, {6,160}*1920, {12,15}*1920, {8,15}*1920a, {8,30}*1920a, {6,30}*1920a, {6,40}*1920a, {12,40}*1920e, {12,40}*1920f, {12,60}*1920a, {12,60}*1920b, {6,40}*1920b, {6,60}*1920, {6,20}*1920a, {6,30}*1920b, {6,30}*1920c, {6,40}*1920c, {24,20}*1920c, {24,20}*1920d, {6,40}*1920d, {6,120}*1920a, {6,20}*1920b, {6,120}*1920b, {12,20}*1920b, {12,20}*1920c, {12,60}*1920c, {24,30}*1920a, {12,30}*1920, {12,40}*1920g, {12,40}*1920h, {12,60}*1920d, {24,20}*1920e, {24,20}*1920f, {24,30}*1920b, {4,60}*1920d, {8,60}*1920e, {8,60}*1920f, {4,30}*1920a, {8,30}*1920d, {8,30}*1920e, {8,30}*1920f, {8,60}*1920g, {8,60}*1920h, {4,120}*1920c, {4,120}*1920d, {8,30}*1920g, {4,60}*1920e, {4,120}*1920e, {4,30}*1920b, {4,120}*1920f, {8,15}*1920b, {4,15}*1920a, {4,30}*1920c, {8,15}*1920c, {12,10}*1920a, {4,30}*1920d
97-fold covers : {2,485}*1940
98-fold covers : {98,10}*1960, {2,490}*1960, {14,70}*1960a, {14,70}*1960b, {14,70}*1960c
99-fold covers : {2,495}*1980, {6,165}*1980
100-fold covers : {2,500}*2000, {4,250}*2000, {20,50}*2000a, {50,20}*2000a, {10,100}*2000a, {10,100}*2000b, {100,10}*2000a, {10,20}*2000a, {10,20}*2000b, {20,10}*2000b, {20,50}*2000b, {20,10}*2000c, {10,20}*2000h, {20,10}*2000h, {4,10}*2000b, {4,20}*2000b, {10,20}*2000j
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (4,5)(6,7);;
s2 := (3,4)(5,6);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s1*s0*s1, s0*s2*s0*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(7)!(1,2);
s1 := Sym(7)!(4,5)(6,7);
s2 := Sym(7)!(3,4)(5,6);
poly := sub<Sym(7)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope