Revise vertices, edges and faces. 1. Identify and count the: i. vertices ii. edges iii. faces

Here are the solutions to the problems: 1. Identify and count the: Object 1 (Dark brown hexagonal prism): i. faces: 8 ii. edges: 18 iii. vertices: 12 Object 2 (Layered square pyramid): i. vertices: 5 ii. edges: 8 iii. faces: 5 Object 3 (Brown rectangular prism/cuboid): i. faces: 6 ii. edges: 12 iii. vertices: 8 Object 4 (Stack of 3 cubes, forming a rectangular prism): i. faces: 6 ii. edges: 12 iii. vertices: 8 Object 5 (Green hexagonal prism): i. faces: 8 ii. edges: 18 iii. vertices: 12 Object 6 (House-like structure: rectangular prism base + triangular prism roof): i. vertices: 10 ii. edges: 17 iii. faces: 9 2. Find or draw pictures of objects with: a. 8 vertices, 12 edges and 6 faces: This describes a rectangular prism (also known as a cuboid or a cube). Drawing description:* Draw a rectangle. Draw another identical rectangle slightly above and to the right of the first. Connect the corresponding vertices of the two rectangles with straight lines. b. 4 vertices, 6 edges and 4 faces: This describes a triangular pyramid (also known as a tetrahedron). Drawing description:* Draw a triangle for the base. From a point above the center of the triangle, draw lines connecting to each of the three vertices of the base. 3. Can a 3-D object have equal numbers of vertices, edges and faces? No, a 3-D object (specifically a polyhedron) cannot have an equal number of vertices, edges, and faces. This is governed by Euler's formula for polyhedra, which states that V - E + F = 2, where V is the number of vertices, E is the number of edges, and F is the number of faces. If V = E = F, then substituting this into the formula would give V - V + V = 2, which simplifies to V = 2. A polyhedron cannot have only 2 vertices, 2 edges, and 2 faces in a non-degenerate form. The answer is No. 3 done, 2 left today. You're making progress.