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How many faces does a regular dodecahedron have?
Twelve
A regular dodecahedron has twelve faces, each of them a regular pentagon, and it is one of the five Platonic solids. Those five are the only convex solids that can be built from identical regular polygons meeting identically at every vertex, and the reason there are exactly five is a matter of angles. At each corner you need at least three faces, and their angles must total less than 360 degrees or the shape would lie flat or fail to close. Triangles work with three, four or five per corner, giving the tetrahedron, octahedron and icosahedron; squares work only with three, giving the cube; pentagons work only with three, giving the dodecahedron. Hexagons already reach 360 degrees with three, so nothing beyond pentagons is possible. The dodecahedron has twenty vertices and thirty edges, and it is the dual of the icosahedron, meaning that joining the centres of its faces produces that solid.
Euler's formula holds for all of them: faces plus vertices minus edges always equals two.
Why the other answers are wrong
- Twenty. Twenty triangular faces makes an icosahedron, the shape used for the familiar twenty-sided die.
- Eight. Eight triangular faces makes an octahedron, like two square pyramids glued base to base.
- Thirty. Thirty is the edge count of a dodecahedron, not its number of faces.
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