Platonic Solids
Faces, edges, vertices, area, and volume of regular solids
About this calculator
The Platonic Solids Calculator reports the faces, edges, and vertices of each of the five regular convex polyhedra — the tetrahedron, cube, octahedron, dodecahedron, and icosahedron — and computes the surface area, volume, circumradius, inradius, midradius, and dihedral angle for any edge length. Every metric is exact, derived from the edge length with 30-digit precision, and the wireframe shows how the faces meet at each vertex. Useful for geometry, crystallography, dice design, and 3D modelling.
How to use the Platonic Solids calculator
- Enter the measurements you know into the input fields.
- Read the computed properties — they update instantly as you type.
- Compare the diagram with your figure to confirm the setup is right.
- Copy the page URL to share the exact calculation.
Common examples
- Tetrahedron, edge 1 → 4 faces, 6 edges, 4 vertices, area √3 ≈ 1.7321, volume ≈ 0.1179
- Cube, edge 2 → 6 faces, 12 edges, 8 vertices, surface area 24, volume 8
- Octahedron, edge 1 → 8 faces, 12 edges, 6 vertices, dihedral angle ≈ 109.47°
- Dodecahedron, edge 1 → 12 faces, 30 edges, 20 vertices, volume ≈ 7.6631
- Icosahedron, edge 1 → 20 faces, 30 edges, 12 vertices, area 5√3 ≈ 8.6603
Frequently asked questions
How does the Platonic Solids calculator work?
Enter the known measurements of your figure and the calculator applies the standard geometric formulas to find the remaining properties, alongside a diagram that reflects your numbers. All values are computed with high-precision arithmetic.
When would I use the Platonic Solids calculator?
It helps with geometry homework, technical drawing, construction and DIY layout, and any situation where you know some measurements of a shape and need the rest.
How accurate are the results?
Formulas are evaluated at 30 significant digits of precision internally, including roots and trigonometric functions. Displayed values are rounded for readability, but the underlying computation does not accumulate floating-point drift.
Can I share a specific calculation with someone else?
Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same figure and results for whoever clicks it.