Polytope of Type {10,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,2}*40
if this polytope has a name.
Group : SmallGroup(40,13)
Rank : 3
Schlafli Type : {10,2}
Number of vertices, edges, etc : 10, 10, 2
Order of s0s1s2 : 10
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{10,2,2} of size 80
{10,2,3} of size 120
{10,2,4} of size 160
{10,2,5} of size 200
{10,2,6} of size 240
{10,2,7} of size 280
{10,2,8} of size 320
{10,2,9} of size 360
{10,2,10} of size 400
{10,2,11} of size 440
{10,2,12} of size 480
{10,2,13} of size 520
{10,2,14} of size 560
{10,2,15} of size 600
{10,2,16} of size 640
{10,2,17} of size 680
{10,2,18} of size 720
{10,2,19} of size 760
{10,2,20} of size 800
{10,2,21} of size 840
{10,2,22} of size 880
{10,2,23} of size 920
{10,2,24} of size 960
{10,2,25} of size 1000
{10,2,26} of size 1040
{10,2,27} of size 1080
{10,2,28} of size 1120
{10,2,29} of size 1160
{10,2,30} of size 1200
{10,2,31} of size 1240
{10,2,32} of size 1280
{10,2,33} of size 1320
{10,2,34} of size 1360
{10,2,35} of size 1400
{10,2,36} of size 1440
{10,2,37} of size 1480
{10,2,38} of size 1520
{10,2,39} of size 1560
{10,2,40} of size 1600
{10,2,41} of size 1640
{10,2,42} of size 1680
{10,2,43} of size 1720
{10,2,44} of size 1760
{10,2,45} of size 1800
{10,2,46} of size 1840
{10,2,47} of size 1880
{10,2,48} of size 1920
{10,2,49} of size 1960
{10,2,50} of size 2000
Vertex Figure Of :
{2,10,2} of size 80
{4,10,2} of size 160
{5,10,2} of size 200
{3,10,2} of size 240
{3,10,2} of size 240
{5,10,2} of size 240
{5,10,2} of size 240
{6,10,2} of size 240
{8,10,2} of size 320
{4,10,2} of size 400
{10,10,2} of size 400
{10,10,2} of size 400
{10,10,2} of size 400
{12,10,2} of size 480
{4,10,2} of size 480
{4,10,2} of size 480
{6,10,2} of size 480
{6,10,2} of size 480
{3,10,2} of size 480
{5,10,2} of size 480
{6,10,2} of size 480
{6,10,2} of size 480
{6,10,2} of size 480
{6,10,2} of size 480
{10,10,2} of size 480
{10,10,2} of size 480
{10,10,2} of size 480
{10,10,2} of size 480
{14,10,2} of size 560
{3,10,2} of size 600
{6,10,2} of size 600
{15,10,2} of size 600
{16,10,2} of size 640
{5,10,2} of size 640
{4,10,2} of size 640
{4,10,2} of size 640
{5,10,2} of size 640
{18,10,2} of size 720
{3,10,2} of size 720
{15,10,2} of size 720
{20,10,2} of size 800
{20,10,2} of size 800
{20,10,2} of size 800
{4,10,2} of size 800
{22,10,2} of size 880
{24,10,2} of size 960
{6,10,2} of size 960
{4,10,2} of size 960
{4,10,2} of size 960
{12,10,2} of size 960
{12,10,2} of size 960
{12,10,2} of size 960
{12,10,2} of size 960
{20,10,2} of size 960
{20,10,2} of size 960
{4,10,2} of size 960
{6,10,2} of size 960
{6,10,2} of size 960
{10,10,2} of size 960
{25,10,2} of size 1000
{5,10,2} of size 1000
{10,10,2} of size 1000
{26,10,2} of size 1040
{28,10,2} of size 1120
{5,10,2} of size 1200
{15,10,2} of size 1200
{6,10,2} of size 1200
{6,10,2} of size 1200
{12,10,2} of size 1200
{30,10,2} of size 1200
{30,10,2} of size 1200
{30,10,2} of size 1200
{32,10,2} of size 1280
{5,10,2} of size 1280
{8,10,2} of size 1280
{8,10,2} of size 1280
{8,10,2} of size 1280
{8,10,2} of size 1280
{10,10,2} of size 1280
{10,10,2} of size 1280
{10,10,2} of size 1280
{4,10,2} of size 1280
{4,10,2} of size 1280
{10,10,2} of size 1280
{34,10,2} of size 1360
{35,10,2} of size 1400
{36,10,2} of size 1440
{3,10,2} of size 1440
{4,10,2} of size 1440
{5,10,2} of size 1440
{8,10,2} of size 1440
{8,10,2} of size 1440
{10,10,2} of size 1440
{10,10,2} of size 1440
{6,10,2} of size 1440
{12,10,2} of size 1440
{3,10,2} of size 1440
{6,10,2} of size 1440
{6,10,2} of size 1440
{15,10,2} of size 1440
{30,10,2} of size 1440
{30,10,2} of size 1440
{38,10,2} of size 1520
{40,10,2} of size 1600
{40,10,2} of size 1600
{40,10,2} of size 1600
{8,10,2} of size 1600
{21,10,2} of size 1680
{35,10,2} of size 1680
{42,10,2} of size 1680
{44,10,2} of size 1760
{9,10,2} of size 1800
{18,10,2} of size 1800
{45,10,2} of size 1800
{46,10,2} of size 1840
{48,10,2} of size 1920
{12,10,2} of size 1920
{15,10,2} of size 1920
{8,10,2} of size 1920
{8,10,2} of size 1920
{24,10,2} of size 1920
{24,10,2} of size 1920
{24,10,2} of size 1920
{24,10,2} of size 1920
{40,10,2} of size 1920
{40,10,2} of size 1920
{4,10,2} of size 1920
{12,10,2} of size 1920
{12,10,2} of size 1920
{20,10,2} of size 1920
{6,10,2} of size 1920
{8,10,2} of size 1920
{8,10,2} of size 1920
{12,10,2} of size 1920
{12,10,2} of size 1920
{20,10,2} of size 1920
{6,10,2} of size 1920
{10,10,2} of size 1920
{4,10,2} of size 2000
{20,10,2} of size 2000
{20,10,2} of size 2000
{20,10,2} of size 2000
{20,10,2} of size 2000
{50,10,2} of size 2000
{50,10,2} of size 2000
{10,10,2} of size 2000
{10,10,2} of size 2000
{10,10,2} of size 2000
{20,10,2} of size 2000
{10,10,2} of size 2000
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {5,2}*20
5-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {20,2}*80, {10,4}*80
3-fold covers : {10,6}*120, {30,2}*120
4-fold covers : {20,4}*160, {40,2}*160, {10,8}*160
5-fold covers : {50,2}*200, {10,10}*200a, {10,10}*200c
6-fold covers : {10,12}*240, {20,6}*240a, {60,2}*240, {30,4}*240a
7-fold covers : {10,14}*280, {70,2}*280
8-fold covers : {40,4}*320a, {20,4}*320, {40,4}*320b, {20,8}*320a, {20,8}*320b, {80,2}*320, {10,16}*320
9-fold covers : {10,18}*360, {90,2}*360, {30,6}*360a, {30,6}*360b, {30,6}*360c
10-fold covers : {100,2}*400, {50,4}*400, {10,20}*400a, {20,10}*400a, {20,10}*400b, {10,20}*400c
11-fold covers : {10,22}*440, {110,2}*440
12-fold covers : {10,24}*480, {40,6}*480, {20,12}*480, {60,4}*480a, {120,2}*480, {30,8}*480, {20,6}*480c, {30,6}*480, {30,4}*480
13-fold covers : {10,26}*520, {130,2}*520
14-fold covers : {20,14}*560, {10,28}*560, {140,2}*560, {70,4}*560
15-fold covers : {50,6}*600, {150,2}*600, {10,30}*600a, {10,30}*600b, {30,10}*600b, {30,10}*600c
16-fold covers : {40,4}*640a, {40,8}*640a, {40,8}*640b, {20,8}*640a, {40,8}*640c, {40,8}*640d, {80,4}*640a, {80,4}*640b, {20,4}*640a, {40,4}*640b, {20,8}*640b, {20,16}*640a, {20,16}*640b, {160,2}*640, {10,32}*640, {10,4}*640b
17-fold covers : {10,34}*680, {170,2}*680
18-fold covers : {10,36}*720, {20,18}*720a, {180,2}*720, {90,4}*720a, {60,6}*720a, {30,12}*720a, {30,12}*720b, {60,6}*720b, {60,6}*720c, {30,12}*720c, {20,4}*720, {30,4}*720, {20,6}*720
19-fold covers : {10,38}*760, {190,2}*760
20-fold covers : {100,4}*800, {200,2}*800, {50,8}*800, {10,40}*800a, {40,10}*800a, {40,10}*800b, {20,20}*800a, {20,20}*800c, {10,40}*800c
21-fold covers : {30,14}*840, {10,42}*840, {70,6}*840, {210,2}*840
22-fold covers : {20,22}*880, {10,44}*880, {220,2}*880, {110,4}*880
23-fold covers : {10,46}*920, {230,2}*920
24-fold covers : {10,48}*960, {80,6}*960, {20,12}*960a, {20,24}*960a, {40,12}*960a, {20,24}*960b, {40,12}*960b, {120,4}*960a, {60,4}*960a, {120,4}*960b, {60,8}*960a, {60,8}*960b, {240,2}*960, {30,16}*960, {20,12}*960b, {20,6}*960e, {60,6}*960a, {30,12}*960a, {30,6}*960, {40,6}*960d, {40,6}*960e, {60,6}*960b, {20,12}*960c, {30,12}*960b, {60,4}*960b, {30,4}*960b, {60,4}*960c, {30,8}*960b, {30,8}*960c
25-fold covers : {250,2}*1000, {10,50}*1000a, {50,10}*1000a, {50,10}*1000b, {10,10}*1000a, {10,10}*1000c, {10,10}*1000d
26-fold covers : {20,26}*1040, {10,52}*1040, {260,2}*1040, {130,4}*1040
27-fold covers : {10,54}*1080, {270,2}*1080, {30,18}*1080a, {30,6}*1080a, {90,6}*1080a, {90,6}*1080b, {30,18}*1080b, {30,6}*1080b, {30,6}*1080c, {30,6}*1080d
28-fold covers : {40,14}*1120, {10,56}*1120, {20,28}*1120, {140,4}*1120, {280,2}*1120, {70,8}*1120
29-fold covers : {10,58}*1160, {290,2}*1160
30-fold covers : {50,12}*1200, {100,6}*1200a, {300,2}*1200, {150,4}*1200a, {20,30}*1200a, {10,60}*1200a, {20,30}*1200b, {30,20}*1200b, {10,60}*1200b, {60,10}*1200b, {60,10}*1200c, {30,20}*1200c
31-fold covers : {10,62}*1240, {310,2}*1240
32-fold covers : {40,8}*1280a, {20,8}*1280a, {40,8}*1280b, {40,4}*1280a, {40,8}*1280c, {40,8}*1280d, {20,16}*1280a, {80,4}*1280a, {20,16}*1280b, {80,4}*1280b, {80,8}*1280a, {40,16}*1280a, {80,8}*1280b, {40,16}*1280b, {40,16}*1280c, {80,8}*1280c, {80,8}*1280d, {40,16}*1280d, {40,16}*1280e, {80,8}*1280e, {80,8}*1280f, {40,16}*1280f, {20,32}*1280a, {160,4}*1280a, {20,32}*1280b, {160,4}*1280b, {20,4}*1280a, {40,4}*1280b, {20,8}*1280b, {20,8}*1280c, {40,8}*1280e, {40,4}*1280c, {40,4}*1280d, {20,8}*1280d, {40,8}*1280f, {40,8}*1280g, {40,8}*1280h, {10,64}*1280, {320,2}*1280, {10,4}*1280a, {20,4}*1280b, {20,4}*1280c, {10,8}*1280c, {10,4}*1280b, {10,8}*1280d, {20,4}*1280d, {20,4}*1280e, {10,4}*1280c, {10,8}*1280e, {10,8}*1280f
33-fold covers : {30,22}*1320, {10,66}*1320, {110,6}*1320, {330,2}*1320
34-fold covers : {20,34}*1360, {10,68}*1360, {340,2}*1360, {170,4}*1360
35-fold covers : {50,14}*1400, {350,2}*1400, {10,70}*1400a, {10,70}*1400b, {70,10}*1400b, {70,10}*1400c
36-fold covers : {10,72}*1440, {40,18}*1440, {20,36}*1440, {180,4}*1440a, {360,2}*1440, {90,8}*1440, {120,6}*1440a, {30,24}*1440a, {60,12}*1440a, {30,24}*1440b, {120,6}*1440b, {120,6}*1440c, {60,12}*1440b, {60,12}*1440c, {30,24}*1440c, {20,18}*1440, {90,4}*1440, {20,4}*1440, {60,4}*1440, {30,8}*1440, {40,6}*1440, {20,12}*1440, {30,6}*1440g, {60,6}*1440c, {30,12}*1440a, {30,12}*1440b, {30,6}*1440h, {60,6}*1440d
37-fold covers : {10,74}*1480, {370,2}*1480
38-fold covers : {20,38}*1520, {10,76}*1520, {380,2}*1520, {190,4}*1520
39-fold covers : {30,26}*1560, {10,78}*1560, {130,6}*1560, {390,2}*1560
40-fold covers : {200,4}*1600a, {100,4}*1600, {200,4}*1600b, {100,8}*1600a, {100,8}*1600b, {400,2}*1600, {50,16}*1600, {10,80}*1600a, {80,10}*1600a, {80,10}*1600b, {20,40}*1600a, {20,20}*1600a, {20,20}*1600c, {20,40}*1600b, {20,40}*1600c, {40,20}*1600c, {40,20}*1600d, {20,40}*1600e, {40,20}*1600e, {40,20}*1600f, {10,80}*1600c
41-fold covers : {10,82}*1640, {410,2}*1640
42-fold covers : {60,14}*1680, {30,28}*1680a, {20,42}*1680a, {10,84}*1680, {70,12}*1680, {140,6}*1680a, {420,2}*1680, {210,4}*1680a
43-fold covers : {10,86}*1720, {430,2}*1720
44-fold covers : {40,22}*1760, {10,88}*1760, {20,44}*1760, {220,4}*1760, {440,2}*1760, {110,8}*1760
45-fold covers : {50,18}*1800, {450,2}*1800, {150,6}*1800a, {150,6}*1800b, {150,6}*1800c, {10,90}*1800a, {10,90}*1800b, {90,10}*1800b, {90,10}*1800c, {30,30}*1800a, {30,30}*1800c, {30,30}*1800e, {30,30}*1800f, {30,30}*1800g, {30,30}*1800i
46-fold covers : {20,46}*1840, {10,92}*1840, {460,2}*1840, {230,4}*1840
47-fold covers : {10,94}*1880, {470,2}*1880
48-fold covers : {60,8}*1920a, {120,4}*1920a, {40,12}*1920a, {20,24}*1920a, {120,8}*1920a, {120,8}*1920b, {120,8}*1920c, {40,24}*1920a, {40,24}*1920b, {40,24}*1920c, {120,8}*1920d, {40,24}*1920d, {60,16}*1920a, {240,4}*1920a, {80,12}*1920a, {20,48}*1920a, {60,16}*1920b, {240,4}*1920b, {80,12}*1920b, {20,48}*1920b, {60,4}*1920a, {120,4}*1920b, {60,8}*1920b, {40,12}*1920b, {20,24}*1920b, {20,12}*1920a, {30,32}*1920, {480,2}*1920, {10,96}*1920, {160,6}*1920, {30,6}*1920a, {40,6}*1920a, {40,12}*1920e, {40,12}*1920f, {60,12}*1920a, {60,12}*1920b, {40,6}*1920b, {60,6}*1920, {20,6}*1920a, {30,6}*1920b, {30,6}*1920c, {40,6}*1920c, {20,24}*1920c, {20,24}*1920d, {40,6}*1920d, {120,6}*1920a, {20,6}*1920b, {120,6}*1920b, {20,12}*1920b, {20,12}*1920c, {60,12}*1920c, {30,24}*1920a, {30,12}*1920, {40,12}*1920g, {40,12}*1920h, {60,12}*1920d, {20,24}*1920e, {20,24}*1920f, {30,24}*1920b, {60,4}*1920d, {60,8}*1920e, {60,8}*1920f, {30,4}*1920a, {30,8}*1920d, {30,8}*1920e, {30,8}*1920f, {60,8}*1920g, {60,8}*1920h, {120,4}*1920c, {120,4}*1920d, {30,8}*1920g, {60,4}*1920e, {120,4}*1920e, {30,4}*1920b, {120,4}*1920f, {10,12}*1920a, {30,4}*1920d
49-fold covers : {10,98}*1960, {490,2}*1960, {70,14}*1960a, {70,14}*1960b, {70,14}*1960c
50-fold covers : {500,2}*2000, {250,4}*2000, {20,50}*2000a, {50,20}*2000a, {10,100}*2000a, {100,10}*2000a, {100,10}*2000b, {10,20}*2000b, {20,10}*2000a, {20,10}*2000b, {50,20}*2000b, {10,20}*2000c, {10,20}*2000h, {20,10}*2000h, {10,4}*2000b, {20,4}*2000b, {20,10}*2000j
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);;
s2 := (11,12);;
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*s2*s0*s2, s1*s2*s1*s2,
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(12)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s1 := Sym(12)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,10);
s2 := Sym(12)!(11,12);
poly := sub<Sym(12)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
to this polytope