Question

A platonic solid has all faces congruent. Given below is one face of a platonic solid. Faces of this solid meet to create six vertices and twelve edges. Visualizing this solid, count the total number of triangles visible on all the faces.

Hint:

When counting the number of triangles in a polyhedron, consider the number of faces and the type of each face.

Answer 1

Step 1: Analyze the Platonic Solid.
The given face of the platonic solid is a triangle, and since all faces are congruent, each face is a triangle. The solid in question is likely a regular tetrahedron, where each face is an equilateral triangle.
Step 2: Count the faces.
A tetrahedron has 4 faces. Since each face is a triangle, the total number of triangles visible on all faces is: \[ \text{Total number of triangles} = 4 \text{ faces} \times 1 \text{ triangle per face} = 4. \]
\[ \boxed{4} \]