Unlock the geometry of icosahedrons with our online calculator. Quickly find the circumradius, inradius, and midradius by simply entering the edge length. Ideal for students, designers, and engineers needing precise measurements for this 20-faced polyhedron.
Formula:
Icosahedron Radii Formulas
Let a be the edge length of the icosahedron.
- Circumradius (R): The distance from the center to any vertex.
R = (a / 4) × √(10 + 2√5) - Inradius (r): The distance from the center to the center of any face.
r = (a / 12) × √3 × (3 + √5) - Midradius (ρ): The distance from the center to the midpoint of any edge.
ρ = (a / 4) × √(5 + 2√5)