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A geometric solid is a portion of space which is completely enclosed, or separated from the rest of space, by some type of surface. The three-dimensional figures with polygon faces are categorized as polyhedra.

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A polyhedron (plural polyhedra) is a three-dimensional solid with flat polygon faces joined at their edges.
The word polyhedron is derived from the Greek poly meaning "many",
and the Indo-European
hedron meaning "seat or face".
A polyhedron's faces are bounding surfaces consisting of portions of intersecting planes.

starsmall A polyhedron has no curved surfaces.
The "faces" (sides) are flat, plane surfaces.

We will be working with polyhedra that are referred to as prisms and pyramids:

prismspyramids

In the polyhedra shown above, the sides of the figures are not all of the same shape or size.
If all of the sides are the same shape and size, the figure is called a regular polyhedron.

The regular polyhedra that we will be seeing are a triangular pyramid whose sides are all equilateral triangles, and a cube (a square prism) whose sides are all squares.

polyhedron

 

There are a total of five such regular polyhedra called the Platonic Solids,
after the ancient Greek philosopher Plato, in whose writings they first appeared.

The Platonic Solids
Tetrahedron
Octahedron
Icosahedron
Cube
Dodecahedron

tetra

octa icosa hexa dodeca
The cube is also called a hexahedron.

While there is no limit to the number of regular two-dimensional polygons,
there is a limit to the number of regular polyhedra! There are only five!

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We will also be dealing with 3-D shapes that are NOT polyhedra:
These solids are not polyhedra since a part, or all, of the figure is curved.
Cylinder
Cone
Sphere
bluecylinder
blueconeN
sphere


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