Math
Regular dodecahedron
Calculate volume and surface area for a regular solid with twelve pentagonal faces.
Calculators / Math / Regular icosahedron
Regular icosahedron calculator
Calculate volume and surface area for a solid with twenty equal triangular faces.
On this page
Volume17.45units³
Surface area34.64units²
Calculator controls
How to calculate
Calculate volume and surface area for a solid with twenty equal triangular faces.
Volume =
5*(3+sqrt(5))*a^3/12 units³Surface area =
5*sqrt(3)*a^2 units²Worked example
- Edge length: 2
- Volume: 17.45 units³
- Surface area: 34.64 units²
Assumptions and limits
All lengths must use one common unit. These are ideal geometric measurements; allowances, thickness, manufacturing tolerances and measurement uncertainty are excluded.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Calculate volume and surface area for a solid with twenty equal triangular faces. Use a single edge length to check models of a regular icosahedron; irregular solids need separate measurements.
When this tool is useful
Use a single edge length to check models of a regular icosahedron; irregular solids need separate measurements.
Understanding your inputs
| Input | Example |
|---|---|
Edge length a | 2 |
Frequently asked questions
Which assumptions matter for this result?
All lengths must use one common unit. These are ideal geometric measurements; allowances, thickness, manufacturing tolerances and measurement uncertainty are excluded.
How can I check the worked example?
Use the displayed example inputs in the stated formula. Keep each quantity in its labelled unit and compare the unrounded result before applying display rounding.