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## Platonic Solids

• Platonic solids are created when the same multisided shape connects multiple times so as to create a three-dimensional object. The same number of shapes come together at each corner of the platonic solid. A classic example is a cube. Each side of the cube is created from a square. Three squares come together at each corner of the cube. Tetrahedrons, octahedrons and icosahedrons are platonic solids with triangular faces. Tetrahedrons have four faces. Octahedrons have eight, and icosahedrons have 20. The final type of platonic solid is the dodecahedron. It has12 pentagon-shaped faces.

## Prisms

• Prisms are a type of polhedra. You identify prisms by their cross sections. The cross section for a prism will be the same all along its length. This means that, if you cut across a prism horizontally, you would see the outline of the same size polygon wherever along the length you make the cut. This polygon is also visible at each end of the prism when intact. Prisms are named for the shape visible at each end and in the cross section. Triangular prisms, pentagonal prisms and square prisms are common. The cube is a special type of square prism.

## Pyramids

• Pyramids are geometric solids with a base and triangular sides that meet at an apex, or point above the base. The base of pyramids may be shaped like any polygon, and pyramids are named for the shape of their base. The famous Egyptian pyramids are square pyramids because they have square bases. Triangular pyramids and pentagonal pyramids are additional examples of this geometric solid. Additionally, pyramids may be described as being right or oblique. When the apex is centered above the base, the pyramid is right. When the apex is not centered, the pyramid is oblique. Finally, if the base has unequal angles and sides, the pyramid is irregular.

## Nonpolyhedra

• Nonpolyhedra have at least one surface that is not flat. Examples of nonpolyhedra include the sphere, which is like a ball or planet, and the torus, which is like a doughnut. Even though cylinders and cones have at least one flat surface, the curvature of these shapes prevents them from being classified as polyhedra.

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