| Czworościan | Sześcian | Ośmiościan | Dwunastościan | Dwudziestościan | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Tetrahedron | Cube | Octahedron | Dodecahedron | Icosahedron | |||||||
| `a` | krawędź – edge length | ||||||||||
| `h` | wysokość – height | `h = (a sqrt(6))/3 = r_c + r_i` | `h = a = 2 r_i` | `h = (a sqrt(6))/3 = 2 r_i` | `h = a sqrt((25 + 11 sqrt(5))/10) = 2 r_i` | `h = ((3 + sqrt(5)) a sqrt(3))/6 = 2 r_i` | |||||
| `A` | powierzchnia całkowita – surface area | `A = a^2 sqrt(3)` | `A = 6 a^2` | `A = 2 a^2 sqrt(3)` | `A = 3 a^2 sqrt(5(5 + 2 sqrt(5)))` | `A = 5 a^2 sqrt(3)` | |||||
| `V` | objętość – volume | `V = (a^3 sqrt(2))/12` | `V = a^3` | `V = (a^3 sqrt(2))/3` | `V = ((7 sqrt(5) + 15) a^3)/4` | `V = (5 (3 + sqrt(5))a^3)/12` | |||||
| `d` | główna przekątna – volume diagonal | `d = a sqrt(3) = 2 r_c` | `d = a sqrt(2) = 2 r_c` | `d = ((sqrt(5) + 1) a sqrt(3))/2 = 2 r_c` | `d = (a sqrt(2(5 + sqrt(5))))/2 = 2 r_c` | ||||||
| `r_c` | promień sfery opisanej – circumsphere radius | `r_c = (a sqrt(6))/4` | `r_c = (a sqrt(3))/2` | `r_c = (a sqrt(2))/2` | `r_c = ((sqrt(5) + 1) a sqrt(3))/4` | `r_c = (a sqrt(2(5 + sqrt(5))))/4` | |||||
| `r_m` | promień sfery pośredniej – midsphere radius | `r_m = (a sqrt(2))/4` | `r_m = (a sqrt(2))/2` | `r_m = a/2` | `r_m = ((3 + sqrt(5)) a)/4` | `r_m = ((1 + sqrt(5)) a)/4` | |||||
| `r_i` | promień sfery wpisanej – insphere radius | `r_i = (a sqrt(6))/12` | `r_i = a/2` | `r_i = (a sqrt(6))/6` | `r_i = a sqrt((25 + 11 sqrt(5))/40)` | `r_i = ((3 + sqrt(5)) a sqrt(3))/12` | |||||
| `A/V` | stosunek powierzchni do objętości – surface-to-volume ratio | `A/V = (6 sqrt(6))/a` | `A/V = 6/a` | `A/V = (3 sqrt(6))/a` | `A/V = (3(7 - 3 sqrt(5))sqrt(5 + 2 sqrt(5)))/a` | `A/V = (3 sqrt(3) (3 - sqrt(5)))/a` |