1. 14 Chapter Area, Pythagorean Theorem, and Volume
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2. 14-3 Geometry in Three Dimensions
Simple Closed Surfaces
Regular Polyhedra
Cylinders and Cones
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3. Simple Closed Surfaces
A simple closed surface has exactly one interior, no holes, and is hollow.
These two figures are not simple, closed surfaces.
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4. Simple Closed Surfaces
Sphere – the set of all points at a given distance from a given point (the center)
Solid – the set of all points on a simple closed surface together with all interior points
Polyhedron – a simple, closed surface made up of polygonal regions (faces). The vertices of the polygonal regions are the vertices of the polyhedron. The sides of the polygonal regions are called the edges of the polyhedron.
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Polyhedra
Polyhedra:
Not polyhedra:
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Prisms
A prism is a polyhedron in which two congruent faces (the bases) lie in parallel planes and the other faces (lateral faces) are bounded by parallelograms.
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Prisms
Right prism – lateral faces are perpendicular to the bases.
Oblique prism – lateral faces are not perpendicular to the bases.
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Pyramids
A pyramid is a polyhedron determined by a polygon and a point not in the plane of the polygon.
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Pyramids
Right pyramid – lateral faces are congruent isosceles triangles.
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Truncated Polyhedron
If one or more corners of a polyhedron is removed by an intersecting plane or planes, the polyhedron is a truncated polyhedron.
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Regular Polyhedra
Convex polyhedron – a polyhedron in which a segment connecting any two points in the interior of the polyhedron is in the interior of the polyhedron.
Regular polyhedron – a convex polyhedron whose faces are congruent regular polygonal regions such that the number of edges that meet at each vertex is the same for all the vertices of the polyhedron.
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Regular Polyhedra
Cube
Tetrahedron
Octahedron
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Regular Polyhedra
Dodecahedron
Icosahedron
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Nets
These patterns can be used to construct the five regular polyhedra.
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Euler’s Formula
What is the relationship between the number of vertices, faces, and edges of a polyhedron?
V + F – E = 2
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Cylinders and Cones
Cylinder – a simple, closed surface that is not a polyhedron; formed as a segment AB parallel to a given line  traces a planar curve other than a polygon.
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Cylinders and Cones
Cone – the union of the line segments connecting a point P with each point of a simple, closed curve, the simple, closed curve, and the interior of the curve.
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