| NAME | VERTICES | EDGES | FACES |
TETRA. BASED VOLUME EQU. F=Edge Freq. |
SHELL GROWTH 2×N×F2 + 2 F=Edge Freq. |
EULER'S EQUATION
V + F = E + 2 V=Num. Vertices F=Num. Faces E=Num. Edges |
V×360° - ∑Surf.A. = 720° |
| Tetrahedron | 1 F3 | 2×(1)× F2 + 2 |
V = 4
F = 4 E = 6 4 + 4 = 6 + 2 |
4×360° - 4×3×60°
1440° - 720° = 720° |
|||
| Octahedron | 4 F3 | 2×(2)× F2 + 2 |
V = 6
F = 8 E = 12 6 + 8 = 12 + 2 |
6×360° - 8×3×60°
2160° - 1440° = 720° |
|||
|
Hexahedron (Cube) |
3 F3 | 2×(3)× F2 + 2 |
V = 8
F = 6 E = 12 8 + 6 = 12 + 2 |
8×360° - 6×4×90°
2880° - 2160° = 720° |
|||
|
Rhombic Dodecahedron |
6 F3 | 2×(6)× F2 + 2 |
V = 14
F = 12 E = 24 14 + 12 = 24 + 2 |
5040° - 4320° = 720° | |||
| Icosahedron | ≈18.51...F3 | 2×(5)× F2 + 2 |
V = 12
F = 20 E = 30 12 + 20 = 30 + 2 |
12×360° - 20×3×60°
4320° - 3600° = 720° |
|||
| Dodecahedron | ≈ 65.02...F3 |
V = 20
F = 12 E = 30 20 + 12 = 30 + 2 |
20×360° - 12×5×108°
7200° - 6480° = 720° |
||||
|
Rhombic Triacontahedron |
≈104.46...F3 |
V = 32
F = 30 E = 60 32 + 30 = 60 + 2 |
11520° - 10800° = 720° |
Copyright September, 2007 by Robert W. Gray