Calculations at a regular icosahedron, a solid with twenty faces, edges of equal length and angles of equal size. The icosahedron is the last of the five Platonic solids.
Enter one value and choose the number of decimal places. Then click Calculate.
Formulas:
A = 5 * a² * √3
V = 5 / 12 * a³ * ( 3 + √5 )
d = 2 * rc
rc = a / 4 * √10 + 2 * √5
rm = a / 4 * ( 1 + √5 )
ri = a / 12 * √3 * ( 3 + √5 )
A/V = 12 * √3 / ( ( 3 + √5 ) * a )
The regular icosahedron is a Platonic solid. Edge length and radius have the same unit (e.g. meter), the area has this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit -1.
Net of an icosahedron, the three-dimensional body is unfolded in two dimensions.
A regular icosahedron is point-symmetrical to its center. It has 15 planes of symmetry and is rotationally symmetrical to a total of 31 axes of rotation. The dual body of the icosahedron is the dodecahedron, of which the icosahedron is the dual body itself. In the icosahedron, five triangles meet at one point, in the dodecahedron, three pentagons meet. If you regularly cut off the corners of an icosahedron, you get the Archimedean solid truncated icosahedron. The intersection of an icosahedron and a dodecahedron is a truncated dodecahedron. If you place matching regular tetrahedra on the side surfaces, you get a great stellated dodecahedron, the last of the four regular star polyhedra. The icosahedron is the "roundest" of all regular polyhedra, it has the largest volume per diameter and the flattest corners.
Icosahedrons are used as twenty-sided dice. Some viruses are icosahedral-shaped, including the rhinovirus, which is responsible for the common cold, but also the dangerous hepatitis B virus and poliovirus.
