Regular Dodecahedron Calculator

Dodecahedron Volume and Surface Area Calculator

Calculate the volume and surface area of a regular dodecahedron. Essential for geometric modeling, crystallography, and advanced mathematical applications.

A dodecahedron is a three-dimensional geometric shape with twelve regular pentagonal faces. This calculator helps you determine its volume and surface area based on the edge length.

Formula

Volume = (15 + 7√5)a³/4
Surface Area = 3a²√(25 + 10√5)

Where:

  • a:length of any edge of the dodecahedron

Understanding the Dodecahedron

The dodecahedron is one of the five Platonic solids, featuring 12 regular pentagonal faces, 30 edges, and 20 vertices. Each vertex is the meeting point of three faces.

Applications

Dodecahedra appear in crystallography, molecular frameworks, and architectural design. They're also used in role-playing games as twelve-sided dice (d12).

Frequently Asked Questions

What makes a dodecahedron regular?

A regular dodecahedron has faces that are all congruent regular pentagons, with the same number of faces meeting at each vertex.

Where are dodecahedra found in nature?

Dodecahedral shapes appear in some viral capsids, crystal structures, and certain molecular frameworks in chemistry.