12.1 Exploring Solids

Polyhedron: Three dimensional closed figure formed by joining three or more polygons Example:

Which of the following are polyhedrons? No Yes Yes Yes No Yes

Face: sides of a polyhedron that enclose a single region of space Edge: a line segment formed by the intersection of two faces Vertex: a point where three or more edges meet

Example: vertex face edge Faces: 6 Vertices: 8 Edges: 12

Identify the number of faces, vertices, and edges for each figure.

Euler’s Theorem: F + V – 2 = E The number of faces F, vertices V, and edges E of a polyhedron are related by F + V – 2 = E

Use Euler’s Theorem to find the unknown number Faces: Vertices: 16 Edges: 22 Faces: 5 Vertices: Edges: 9 Faces: Vertices: 10 Edges: 15 Faces: 20 Vertices: 12 Edges: 8 7 6 30

A polyhedron is regular if all of its faces are congruent regular polygons. A polyhedron is convex if any two points on its surface can be connected by a segment that lies entirely inside or on the polyhedron. regular convex irregular concave

Cross Section: the intersection of the plane and the solid

Describe the shape formed by the intersection of the plane and the cube pentagon triangle square