What shape are the faces of a dodecahedron?
Conditions
- Must have exactly 12 faces
- All faces must be pentagons
Reasoning, step by step
- Identify the 3D dodecahedron.
- Observe its unfolding into a 2D net.
- Count the faces and identify their shape.
Example
A teal 3D dodecahedron unfolds flat into a 2D net composed of 12 connected pentagons.
Common misconceptions
- Thinking a dodecahedron has 12 sides (edges) instead of 12 faces.
- Confusing pentagons with hexagons.
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Related questions
A triangular pyramid net consists of four triangular faces. The clip also shows that the same triangular pyramid can be unfolded into more than one net layout while preserving the same face count and face types.
Conditions: The solid is a triangular pyramid.; The net contains four triangles.
A polyhedron net is a flat layout obtained by cutting along edges of a 3D solid and unfolding it so that all faces remain connected in one piece. In this clip, the example shown is a rectangular prism whose six rectangular faces become one connected planar figure.
Conditions: The object is a 3D solid (polyhedron).; The faces are laid flat.; The resulting faces form one connected complex polygon.
A hexagonal prism net is composed of two hexagonal bases and six lateral faces. In the visual example, the six lateral faces appear as rectangles connecting the two hexagons in the unfolded layout.
Conditions: The solid is a hexagonal prism.; The net includes two hexagon bases and six lateral faces.
The same polyhedron can have multiple valid nets because changing how the net is oriented on the page or choosing different edges to cut does not change which solid it represents. Different unfoldings of the same rectangular prism are still nets of that same solid.
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A rectangular prism has six rectangular faces, and in the nets shown these six rectangles remain visible after unfolding. The narration also points out that the rectangles occur in pairs, matching opposite faces of the prism.
Conditions: The solid is a rectangular prism.; The net shows all faces without overlap.
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