The dodecahedron can be constructed from the repetitive folding of _____.A.squaresB.equilateral trianglesC.regular pentagonsD.triangles

Break Down the Problem

1. Identify the geometric shape in question: a dodecahedron.
2. Determine the shape of the faces of a dodecahedron.
3. Consider the options provided to find which shape can construct a dodecahedron.

Relevant Concepts

• A dodecahedron is a type of polyhedron that has 12 flat faces.
• Each face of a dodecahedron is a regular polygon.

Analysis and Detail

1. A dodecahedron specifically has 12 faces, all of which are regular pentagons.
2. The term "repetitive folding" suggests that we are looking for a shape that can be utilized to construct the faces of the dodecahedron through some folding technique.

Verify and Summarize

• Upon reviewing the definitions and properties:
  • Squares (4 sides) and triangles (3 sides) cannot comprise the faces of a dodecahedron.
  • Equilateral triangles can construct different polyhedra but not a dodecahedron.
  • Regular pentagons, however, fit perfectly since they are the only shapes that can form the 12 faces of a dodecahedron.

Final Answer

The dodecahedron can be constructed from the repetitive folding of C. regular pentagons.