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 |
|
||
41 |
|
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 |
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