Icosahedron Calculator

A regular icosahedron is a solid with 20 identical equilateral-triangle faces — another of the five Platonic solids, and the shape behind many 20-sided dice and geodesic dome designs.

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What Is a Regular Icosahedron Calculator?

A regular icosahedron is a solid with 20 identical equilateral-triangle faces — another of the five Platonic solids, and the shape behind many 20-sided dice and geodesic dome designs. This calculator finds the volume and surface area from a single edge length.

How to Use This Regular Icosahedron Calculator

  1. Measure one edge of the icosahedron (all edges are equal in a regular icosahedron).
  2. Enter the edge length into the field above.
  3. Click Calculate to get the volume and surface area.

Formula

Worked Example

A 20-sided die (d20) has an edge length of 1 cm. Volume = (5(3+√5)/12) × 1³ ≈ 2.18 cm³. Surface Area = 5√3 × 1² ≈ 8.66 cm².

Frequently Asked Questions

What is an icosahedron?

It's a 3D shape with 20 equilateral triangular faces, 12 vertices, and 30 edges — one of the five Platonic solids.

How is icosahedron volume calculated?

Volume = (5(3+√5))/12 × edge length³, derived from its regular triangular-faced geometry.

Where is this shape commonly seen?

A 20-sided die (d20) used in tabletop gaming is a classic icosahedron, and the shape appears in some virus capsid structures in biology.

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