Section 6.2 – Spatial Relationships

Polyhedron – a closed spatial figure composed of polygons, called the faces of the polyhedron.

The intersections of the faces are called the edges.

The vertices of the faces are called the vertices of the polygon.

Regular polyhedron – all of the faces are regular polygons.

Platonic Solids (pg. 387)

Tetrahedron – 4 faces

Hexahedron (cube) – 6 faces

Octahedron – 8 faces

Dodecahedron – 12 faces

Icosahedron – 20 faces

Parallel planes – two planes are parallel iff they do not intersect

Line Perpendicular to a Plane – A line is perpendicular to a plane at point P iff it is perpendicular to every line in the plane that passes through P

A Line Parallel to a Plane – A line that is not contained in a given plane is parallel to the plane iff it is parallel to a line contained in the plane.

Dihedral Angle – the figure formed by two half-planes with a common edge. Each half-plane is called a face of the angle, and the common edge of the half-planes is called the edge of the angle.

Measure of a Dihedral Angle – the measure of a dihedral angle is the measure of the angle formed by two rays that are on the faces and that are perpendicular to the edge.