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What is Polyhedra?

• Polyhedra, like the example shown, is a
  3-dimensional solid whose surfaces are flat. Many
  everyday objects, such as a milk carton or filing
  cabinet are polyhedral. A cup or a couch arent
  polyhedral because some or all of their sides are
  curved instead of being a flat plane.

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Criteria For Being a Polyhedra

• UNIFORM POLYHEDRA
• Each face is a regular polygon (all sides are the
  same length and angles between sides are equal).
• At any corner on the solid the same number of
  polygons are joined together.
• All the faces on it are identical to each other.
• It has no bumps, dents, spikes, etc.

• Archimedean Solids Polyhedra
• All faces are regular polygons.
• Around each corner are the same number of
  polygons in the same order
• The polyhedra has no bumps, spikes, dents, etc.

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Regular Uniform Polyhedra
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Regular Uniform Polyhedra Examples

• Although, my chart only shows the most common
  Uniform Polyhedra, there are at least 120 of
  them. The ones shown here are also four of the
  more common, everyday Uniform Polyhedra. The blue
  one is a regular dodecahedron, the red one below
  it is a tetrahedron. The yellow one on the other
  side is a hexahedron, and the red one below it is
  a icosahedron.

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Archimedean Polyhedra

• These polyhedra often look like stained-glass
  balls. One way of making these is to chop the
  corners off of a Regular uniform polyhedra. The
  cube and octahedron are Archimedeans too, because
  the criteria for an Archimedean are more general
  than those for a Regular uniform polyhedra.Some
  are made by fitting triangles along a Regular
  polyhedra, which shows that all polyhedra models
  are mae from Regular Polyhedra.
• The Archimedean shown here is constructed from
  the hexahedron and octahedron, which are also
  Archimedeans.

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Archimedean Polyhedra Examples
The duals of an Archimedean snub dodecahedron are
pictured here.These are created by fitting
triangles along the edges of a dodecahedron.
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Snub Polyhedra

• There are only 11 existing Regular Uniform
  Snub Polyhedra.They are all also made from
  Regular Uniform Polyhedra, but most Snubs are
  much more complex. Many snubs are combined with
  Archimedeans to make different typed of
  polyhedra. They are made by adding points and
  edges to the Regular polyhedras.

Shown above is a normal snub dodecadodecahedron
Shown above is a small snub icosicosidodecahedron
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Snub Polyhedra Examples
To the left you see a snub hexahedron. To the
right is a great dirhombicosidodecahedron
Above is a small retrosnub icosicosidodecahedron.
Above is a great inverted snub icosadodecahedron
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Why learn about Polyhedra?

• Polyhedra are beautiful to look at and may make
  future math classes easier.
• Also polyhedra is fun to make! There are several
  ways to make models from using paper, to origami,
  to computer graphics!
• Go to htt//www.geocities.com
• to learn more about how to make polyhedra
  models!