Waterman's Polyhedral Mensuration chart

copyright by by Steve Waterman June 2010

All Polyhedron Volumes = the shortest edge3 times below values.

   PLATONIC - ARCHIMEDEAN - JOHNSON SOLIDS

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Click on polyhedra name to view rotatable polygon.

 

PLATONIC SOLIDS

1
tetrahedron
0.117851130198
2
1.000000000000
3
0.471404520791
4
7.663118960625
5
6.977982463099

ARCHIMEDEAN SOLIDS

1

truncated tetrahedron
4.625539099587
2
cuboctahedron
6.485128162886
3
truncated octahedron
7.874985950524
4
truncated cube
13.599663291075
5
rhombicuboctahedron
8.714045207910
6
truncated cuboctahedron
41.798989873224
7
snub cube
7.889477399975
8
icosidodecahedron
13.835525936250
9
truncated icosidodecahedron
55.287730758123
10
truncated dodecahedron
85.039664559374
11
rhombicosidodecahedron
41.615323782499
12
truncated icosidodecahedron
206.803398874995
13
snub dodecahedron
37.616649962734

JOHNSON SOLIDS

1
square pyramid
0.235702260396
2
0.301502832396
3
1.178511301978
4
1.942809041582
5
2.324045318333
6
pentagonal rotunda
6.917762968125
7
0.550863832090
8
1.235702260396
9
2.021980232985
10
1.192702242232
11
1.880192158229
12
0.235702260396
13
0.603005664792
14
0.668714962288
15
1.471404520791
16
elongated pentagonal dipyramid
2.323483065381
17
1.428404502628
18
3.776587513331
19
6.771236166328
20
10.018254161271
21
elongated pentagonal rotunda
14.611971811063
22
3.516053090938
23
6.210765792039
24
9.073333193880
25
13.667050843672
26
0.866025403784
27
2.357022603955
28
3.885618083164
29
3.885618083164
30
9.241808286458
31
pentagonal gyrobicupola
4.648090636666
32
13.835525936249
33
9.241808286458
34
13.835525936249
35
4.955098815308
36
elongated triangular gyrobicupola
4.955098815308
37
1.398966325966
38
12.342299479605
39
12.342299479605
40
16.936017129396
41
elongated pentagonal gyrocupolarotunda
16.936017129396
42
21.529734779188
43
21.529734779188
44
4.694564392916
45
8.153574833621
46
gyroelongated pentagonal bicupola
11.397378512213
47
15.991096162005
48
20.584813811796
49
0.668714962288
50
0.904417222683
51
triaugmented triangular prism
1.140119483079
52
1.956179660984
53
2.191881921380
54
2.833778471749
55
3.069480732144
56
metabiaugmented hexagonal prism
3.069480732144
57
2.981865408195
58
7.964621793020
59
8.266124625416
60
8.266124625416
61
triaugmented dodecahedron
8.567627457812
62
1.578689325833
63
1.277186493437
64
1.395037623635
65
3.889087296526
66
augmented truncated cube
15.542472332657
67
17.485281374239
68
87.363709877705
69
89.687755196038
70
89.687755196038
71
triaugmented truncated dodecahedron
92.011800514371
72
41.615323782498
73
41.615323782498
74
41.615323782498
75
39.291278464165
76
diminished rhombicosidodecahedron
39.291278464165
77
39.291278464165
78
39.291278464165
79
39.291278464165
80
39.291278464165
81
metabidiminished rhombicosidodecahedron
39.291278464165
82
39.291278464165
83
34.643187827499
84
0.859493646191
85
3.601222009734
86
sphenocorona
1.515351639976
87
1.751053900372
88
1.948108228859
89
2.912910414540
90
3.777645341859
91
bilunabirotunda
3.093717649792
92
5.108745973750

SYMMETRIES      

Cs Ci C2 C3 C4 C5 C6 C10 C2v C3v C4v C5v C6v C2h C3h C4h C5h C6h C10h

D2 D3 D4 D5 D6 D10 D2v D3v D4v D5v D6v D10v D2h D3h D4h D5h D6h D10h

S2 S4 S6 S10 S12 S20 T Td Th O Oh I Ih

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