A regular icosahedron has 20 congruent equilateral triangular faces and a single shared edge length .
The volume follows V= rac{5(3+sqrt{5})}{12}a^3, so the solid scales cubically with the edge length.
That makes it useful for checking model dimensions, geometry problems, and Platonic-solid comparisons.
Calculate the volume of a regular octahedron from one edge length, then inspect related geometric measures and a compact solid sketch.
Calculate the volume of a regular dodecahedron from its edge length, with supporting surface area, circumradius, and a compact solid preview.
Calculate the volume of a cone from its radius and height, inspect a compact cone sketch, and verify the one-third cylinder rule.