Polytope of Type {8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8}*16
Also Known As : octagon, {8}. if this polytope has another name.
Group : SmallGroup(16,7)
Rank : 2
Schlafli Type : {8}
Number of vertices, edges, etc : 8, 8
Order of s0s1 : 8
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{8,2} of size 32
{8,4} of size 64
{8,4} of size 64
{8,6} of size 96
{8,3} of size 96
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Vertex Figure Of :
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{24,8} of size 768
{24,8} of size 768
{48,8} of size 768
{48,8} of size 768
{48,8} of size 768
{48,8} of size 768
{48,8} of size 768
{48,8} of size 768
{12,8} of size 768
{12,8} of size 768
{24,8} of size 768
{12,8} of size 768
{24,8} of size 768
{24,8} of size 768
{24,8} of size 768
{12,8} of size 768
{12,8} of size 768
{12,8} of size 768
{12,8} of size 768
{6,8} of size 768
{6,8} of size 768
{6,8} of size 768
{12,8} of size 768
{12,8} of size 768
{6,8} of size 768
{12,8} of size 768
{6,8} of size 768
{6,8} of size 768
{12,8} of size 768
{6,8} of size 768
{6,8} of size 768
{6,8} of size 768
{12,8} of size 768
{12,8} of size 768
{24,8} of size 768
{24,8} of size 768
{24,8} of size 768
{24,8} of size 768
{6,8} of size 768
{24,8} of size 768
{12,8} of size 768
{24,8} of size 768
{12,8} of size 768
{24,8} of size 768
{24,8} of size 768
{12,8} of size 768
{12,8} of size 768
{12,8} of size 768
{12,8} of size 768
{12,8} of size 768
{6,8} of size 768
{12,8} of size 768
{12,8} of size 768
{6,8} of size 768
{12,8} of size 768
{6,8} of size 768
{6,8} of size 768
{8,8} of size 784
{8,8} of size 784
{14,8} of size 784
{14,8} of size 784
{50,8} of size 800
{10,8} of size 800
{52,8} of size 832
{52,8} of size 832
{54,8} of size 864
{27,8} of size 864
{6,8} of size 864
{6,8} of size 864
{56,8} of size 896
{56,8} of size 896
{28,8} of size 896
{56,8} of size 896
{56,8} of size 896
{28,8} of size 896
{58,8} of size 928
{60,8} of size 960
{60,8} of size 960
{10,8} of size 960
{10,8} of size 960
{15,8} of size 960
{30,8} of size 960
{6,8} of size 960
{10,8} of size 960
{10,8} of size 960
{6,8} of size 960
{15,8} of size 960
{15,8} of size 960
{30,8} of size 960
{30,8} of size 960
{62,8} of size 992
{3,8} of size 1008
{12,8} of size 1008
{21,8} of size 1008
{21,8} of size 1008
{66,8} of size 1056
{33,8} of size 1056
{68,8} of size 1088
{68,8} of size 1088
{70,8} of size 1120
{36,8} of size 1152
{4,8} of size 1152
{12,8} of size 1152
{72,8} of size 1152
{72,8} of size 1152
{72,8} of size 1152
{8,8} of size 1152
{24,8} of size 1152
{8,8} of size 1152
{8,8} of size 1152
{24,8} of size 1152
{24,8} of size 1152
{72,8} of size 1152
{8,8} of size 1152
{24,8} of size 1152
{36,8} of size 1152
{4,8} of size 1152
{12,8} of size 1152
{9,8} of size 1152
{18,8} of size 1152
{36,8} of size 1152
{36,8} of size 1152
{18,8} of size 1152
{18,8} of size 1152
{36,8} of size 1152
{36,8} of size 1152
{18,8} of size 1152
{18,8} of size 1152
{18,8} of size 1152
{36,8} of size 1152
{36,8} of size 1152
{18,8} of size 1152
{4,8} of size 1152
{4,8} of size 1152
{6,8} of size 1152
{6,8} of size 1152
{6,8} of size 1152
{8,8} of size 1152
{8,8} of size 1152
{12,8} of size 1152
{74,8} of size 1184
{76,8} of size 1216
{76,8} of size 1216
{78,8} of size 1248
{39,8} of size 1248
{40,8} of size 1280
{20,8} of size 1280
{40,8} of size 1280
{40,8} of size 1280
{40,8} of size 1280
{80,8} of size 1280
{80,8} of size 1280
{80,8} of size 1280
{80,8} of size 1280
{80,8} of size 1280
{80,8} of size 1280
{20,8} of size 1280
{20,8} of size 1280
{40,8} of size 1280
{20,8} of size 1280
{40,8} of size 1280
{40,8} of size 1280
{40,8} of size 1280
{5,8} of size 1280
{10,8} of size 1280
{10,8} of size 1280
{20,8} of size 1280
{20,8} of size 1280
{20,8} of size 1280
{20,8} of size 1280
{20,8} of size 1280
{20,8} of size 1280
{20,8} of size 1280
{20,8} of size 1280
{10,8} of size 1280
{10,8} of size 1280
{10,8} of size 1280
{10,8} of size 1280
{6,8} of size 1296
{8,8} of size 1296
{82,8} of size 1312
{84,8} of size 1344
{84,8} of size 1344
{21,8} of size 1344
{42,8} of size 1344
{4,8} of size 1344
{4,8} of size 1344
{12,8} of size 1344
{12,8} of size 1344
{28,8} of size 1344
{28,8} of size 1344
{28,8} of size 1344
{28,8} of size 1344
{6,8} of size 1344
{6,8} of size 1344
{7,8} of size 1344
{4,8} of size 1344
{4,8} of size 1344
{6,8} of size 1344
{6,8} of size 1344
{6,8} of size 1344
{6,8} of size 1344
{8,8} of size 1344
{8,8} of size 1344
{8,8} of size 1344
{8,8} of size 1344
{8,8} of size 1344
{8,8} of size 1344
{8,8} of size 1344
{8,8} of size 1344
{12,8} of size 1344
{12,8} of size 1344
{12,8} of size 1344
{12,8} of size 1344
{12,8} of size 1344
{12,8} of size 1344
{42,8} of size 1344
{42,8} of size 1344
{4,8} of size 1344
{4,8} of size 1344
{6,8} of size 1344
{6,8} of size 1344
{6,8} of size 1344
{6,8} of size 1344
{8,8} of size 1344
{8,8} of size 1344
{14,8} of size 1344
{14,8} of size 1344
{86,8} of size 1376
{44,8} of size 1408
{88,8} of size 1408
{88,8} of size 1408
{88,8} of size 1408
{88,8} of size 1408
{44,8} of size 1408
{90,8} of size 1440
{45,8} of size 1440
{6,8} of size 1440
{6,8} of size 1440
{15,8} of size 1440
{30,8} of size 1440
{4,8} of size 1440
{4,8} of size 1440
{4,8} of size 1440
{6,8} of size 1440
{8,8} of size 1440
{8,8} of size 1440
{8,8} of size 1440
{8,8} of size 1440
{8,8} of size 1440
{10,8} of size 1440
{10,8} of size 1440
{3,8} of size 1440
{4,8} of size 1440
{4,8} of size 1440
{4,8} of size 1440
{5,8} of size 1440
{5,8} of size 1440
{6,8} of size 1440
{6,8} of size 1440
{8,8} of size 1440
{8,8} of size 1440
{8,8} of size 1440
{10,8} of size 1440
{10,8} of size 1440
{10,8} of size 1440
{10,8} of size 1440
{10,8} of size 1440
{10,8} of size 1440
{10,8} of size 1440
{10,8} of size 1440
{10,8} of size 1440
{10,8} of size 1440
{92,8} of size 1472
{92,8} of size 1472
{94,8} of size 1504
{98,8} of size 1568
{14,8} of size 1568
{8,8} of size 1568
{8,8} of size 1568
{14,8} of size 1568
{14,8} of size 1568
{100,8} of size 1600
{100,8} of size 1600
{25,8} of size 1600
{25,8} of size 1600
{20,8} of size 1600
{4,8} of size 1600
{4,8} of size 1600
{20,8} of size 1600
{102,8} of size 1632
{51,8} of size 1632
{52,8} of size 1664
{104,8} of size 1664
{104,8} of size 1664
{104,8} of size 1664
{104,8} of size 1664
{52,8} of size 1664
{15,8} of size 1680
{20,8} of size 1680
{35,8} of size 1680
{35,8} of size 1680
{106,8} of size 1696
{108,8} of size 1728
{108,8} of size 1728
{27,8} of size 1728
{54,8} of size 1728
{54,8} of size 1728
{54,8} of size 1728
{12,8} of size 1728
{12,8} of size 1728
{12,8} of size 1728
{12,8} of size 1728
{12,8} of size 1728
{12,8} of size 1728
{12,8} of size 1728
{12,8} of size 1728
{110,8} of size 1760
{56,8} of size 1792
{28,8} of size 1792
{56,8} of size 1792
{56,8} of size 1792
{56,8} of size 1792
{112,8} of size 1792
{112,8} of size 1792
{112,8} of size 1792
{112,8} of size 1792
{112,8} of size 1792
{112,8} of size 1792
{28,8} of size 1792
{28,8} of size 1792
{56,8} of size 1792
{28,8} of size 1792
{56,8} of size 1792
{56,8} of size 1792
{56,8} of size 1792
{7,8} of size 1792
{7,8} of size 1792
{7,8} of size 1792
{7,8} of size 1792
{114,8} of size 1824
{57,8} of size 1824
{116,8} of size 1856
{116,8} of size 1856
{118,8} of size 1888
{60,8} of size 1920
{120,8} of size 1920
{120,8} of size 1920
{120,8} of size 1920
{120,8} of size 1920
{60,8} of size 1920
{15,8} of size 1920
{30,8} of size 1920
{60,8} of size 1920
{60,8} of size 1920
{30,8} of size 1920
{30,8} of size 1920
{60,8} of size 1920
{60,8} of size 1920
{30,8} of size 1920
{30,8} of size 1920
{30,8} of size 1920
{60,8} of size 1920
{60,8} of size 1920
{30,8} of size 1920
{15,8} of size 1920
{30,8} of size 1920
{30,8} of size 1920
{30,8} of size 1920
{30,8} of size 1920
{15,8} of size 1920
{10,8} of size 1920
{6,8} of size 1920
{10,8} of size 1920
{12,8} of size 1920
{12,8} of size 1920
{12,8} of size 1920
{20,8} of size 1920
{20,8} of size 1920
{6,8} of size 1920
{12,8} of size 1920
{20,8} of size 1920
{20,8} of size 1920
{5,8} of size 1920
{5,8} of size 1920
{6,8} of size 1920
{12,8} of size 1920
{122,8} of size 1952
{124,8} of size 1984
{124,8} of size 1984
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4}*8
4-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {16}*32
3-fold covers : {24}*48
4-fold covers : {32}*64
5-fold covers : {40}*80
6-fold covers : {48}*96
7-fold covers : {56}*112
8-fold covers : {64}*128
9-fold covers : {72}*144
10-fold covers : {80}*160
11-fold covers : {88}*176
12-fold covers : {96}*192
13-fold covers : {104}*208
14-fold covers : {112}*224
15-fold covers : {120}*240
16-fold covers : {128}*256
17-fold covers : {136}*272
18-fold covers : {144}*288
19-fold covers : {152}*304
20-fold covers : {160}*320
21-fold covers : {168}*336
22-fold covers : {176}*352
23-fold covers : {184}*368
24-fold covers : {192}*384
25-fold covers : {200}*400
26-fold covers : {208}*416
27-fold covers : {216}*432
28-fold covers : {224}*448
29-fold covers : {232}*464
30-fold covers : {240}*480
31-fold covers : {248}*496
32-fold covers : {256}*512
33-fold covers : {264}*528
34-fold covers : {272}*544
35-fold covers : {280}*560
36-fold covers : {288}*576
37-fold covers : {296}*592
38-fold covers : {304}*608
39-fold covers : {312}*624
40-fold covers : {320}*640
41-fold covers : {328}*656
42-fold covers : {336}*672
43-fold covers : {344}*688
44-fold covers : {352}*704
45-fold covers : {360}*720
46-fold covers : {368}*736
47-fold covers : {376}*752
48-fold covers : {384}*768
49-fold covers : {392}*784
50-fold covers : {400}*800
51-fold covers : {408}*816
52-fold covers : {416}*832
53-fold covers : {424}*848
54-fold covers : {432}*864
55-fold covers : {440}*880
56-fold covers : {448}*896
57-fold covers : {456}*912
58-fold covers : {464}*928
59-fold covers : {472}*944
60-fold covers : {480}*960
61-fold covers : {488}*976
62-fold covers : {496}*992
63-fold covers : {504}*1008
65-fold covers : {520}*1040
66-fold covers : {528}*1056
67-fold covers : {536}*1072
68-fold covers : {544}*1088
69-fold covers : {552}*1104
70-fold covers : {560}*1120
71-fold covers : {568}*1136
72-fold covers : {576}*1152
73-fold covers : {584}*1168
74-fold covers : {592}*1184
75-fold covers : {600}*1200
76-fold covers : {608}*1216
77-fold covers : {616}*1232
78-fold covers : {624}*1248
79-fold covers : {632}*1264
80-fold covers : {640}*1280
81-fold covers : {648}*1296
82-fold covers : {656}*1312
83-fold covers : {664}*1328
84-fold covers : {672}*1344
85-fold covers : {680}*1360
86-fold covers : {688}*1376
87-fold covers : {696}*1392
88-fold covers : {704}*1408
89-fold covers : {712}*1424
90-fold covers : {720}*1440
91-fold covers : {728}*1456
92-fold covers : {736}*1472
93-fold covers : {744}*1488
94-fold covers : {752}*1504
95-fold covers : {760}*1520
97-fold covers : {776}*1552
98-fold covers : {784}*1568
99-fold covers : {792}*1584
100-fold covers : {800}*1600
101-fold covers : {808}*1616
102-fold covers : {816}*1632
103-fold covers : {824}*1648
104-fold covers : {832}*1664
105-fold covers : {840}*1680
106-fold covers : {848}*1696
107-fold covers : {856}*1712
108-fold covers : {864}*1728
109-fold covers : {872}*1744
110-fold covers : {880}*1760
111-fold covers : {888}*1776
112-fold covers : {896}*1792
113-fold covers : {904}*1808
114-fold covers : {912}*1824
115-fold covers : {920}*1840
116-fold covers : {928}*1856
117-fold covers : {936}*1872
118-fold covers : {944}*1888
119-fold covers : {952}*1904
120-fold covers : {960}*1920
121-fold covers : {968}*1936
122-fold covers : {976}*1952
123-fold covers : {984}*1968
124-fold covers : {992}*1984
125-fold covers : {1000}*2000
Permutation Representation (GAP) :
s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(8)!(2,3)(4,5)(6,7);
s1 := Sym(8)!(1,2)(3,4)(5,6)(7,8);
poly := sub<Sym(8)|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 >;
References : None.
to this polytope