Section 12-1 Exploring Solids

Polyhedron Three dimensional closed figure formed by joining three or more polygons at their side. Plural: polyhedra

Parts of a Polyhedron

Face: Each polygon of the polyhedron Edge: A line segment along which two faces meet Vertex: A point where three or more edges meet

Regular polyhedron Has faces that are congruent regular polygons Example:

Convex Polyhedron If any two points on its surface can be connected by a segment that lies entirely inside or outside the polyhedron

Concave Polyhedron If the segment goes outside the polyhedron

Cross Section Intersection of a plane and a solid

A plane and a solid’s intersection forms different shapes.

Examples of a Plane and a Cube’s Cross Sections Square Triangle Trapezoid

Example of a Plane and a Sphere’s Cross Section Circle

Euler’s Theorem The number of faces (F), vertices (V), and edges (E) of a polyhedron are related by the formula:

Platonic Solids Five regular polyhedra: 1. Tetrahedron: 4 faces 2. Cube: 6 faces 3. Octahedron: 8 faces 4. Dodecahedron: 12 faces 5.Icosahedron: 20 faces

Regular Tetrahedron ____ faces, ____ vertices, ____ edges 464

Cube ____ faces, ____ vertices, ____ edges 8126

Regular Octahedron ____ faces, ____ vertices, ____ edges 6128

Regular Dodecahedron ____ faces, ____ vertices, ____ edges

Regular Icosahedron ____ faces, ____ vertices, ____ edges