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polyhedron

a solid that is bounded by polygons, called faces, that enclose a single region of space

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edge

an edge of a polyhedron is a line segment formed by the intersection of two faces

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vertex

a vertex of a polyhedron is a point where three or more edges meet

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regular

if a polyhedron is regular if all of its faces are congruent regular polygons

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convex

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

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cross section

the of intersection of a plane and a solid

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platonic solids

-tetrahedron (4 faces)

-octahedron (8 faces)

-dodecahedron (12 faces)

-icosahedron (20 faces)

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Euler's Theorem

F + V = E + 2

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Volume Congruence Postulate

if two polyhedra are congruent, then they have the same volume

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Volume Addition Postulate

the volume of a solid is the sum of the volumes of all its non-overlapping parts

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Cavalieri's Principle

if two solids have the same height and the same cross-sectional area at every level, then they have the same volume

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volume of a prism or cylinder

V=Bh

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volume of a pyramid or cone

V=(1/3)Bh

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sphere

the locus of points in space that are a given distance from a point (center of the sphere)

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radius of a sphere

a segment from the center to a point on the sphere

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chord of a sphere

a segment whose endpoints are on the sphere

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similar solids

two solids with equal ratios of corresponding linear measures, such as heights or radii

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Similar Solids Theorem

if two similar solids have a scale factor of a:b, then corresponding areas have a ratio of a^2:b^2, and corresponding volumes have a ratio of a^3:b^3

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