Question

1. complete the missing values for the cube. then, make at least two observations about the number of faces, edges, and vertices in a platonic solid.

Explanation:

Step1: Recall cube properties

A cube is a Platonic solid. For a cube, the number of faces $F = 6$, the number of edges $E=12$, and the number of vertices $V = 8$.

Step2: Make observations

Observation 1: The number of edges is twice the number of faces ($12 = 2\times6$).
Observation 2: Using Euler's formula for polyhedra $F+V - E=2$. Substituting $F = 6$, $V = 8$, and $E = 12$ gives $6 + 8-12=2$.

Answer:

Faces: 6, Edges: 12, Vertices: 8. Observations: 1. The number of edges is twice the number of faces. 2. Euler's formula $F + V-E=2$ holds.