Math
Regular icosahedron
Calculate volume and surface area for a solid with twenty equal triangular faces.
Calculators / Math / Regular dodecahedron
Regular dodecahedron calculator
Calculate volume and surface area for a regular solid with twelve pentagonal faces.
On this page
Volume61.3units³
Surface area82.58units²
Calculator controls
How to calculate
Calculate volume and surface area for a regular solid with twelve pentagonal faces.
Volume =
(15+7*sqrt(5))*a^3/4 units³Surface area =
3*sqrt(25+10*sqrt(5))*a^2 units²Worked example
- Edge length: 2
- Volume: 61.3 units³
- Surface area: 82.58 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 regular solid with twelve pentagonal faces. Only a regular dodecahedron is supported: all edges and all pentagonal faces must be equal.
When this tool is useful
Only a regular dodecahedron is supported: all edges and all pentagonal faces must be equal.
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.