Polyhedrons Polyhedra are beautiful 3 D geometrical figures

Polyhedrons Polyhedra are beautiful 3 -D geometrical figures that have fascinated philosophers, mathematicians and artists for millennia.

Polyhedra • In geometry, a polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat faces and straight edges. The word polyhedron comes from the Classical Greek πολύεδρον, as poly(stem of πολύς, "many") + -hedron (form of έδρα, "base", "seat", or "face").

Polytypes • A polyhedron is a 3 -dimensional example of the more general polytope in any number of dimensions. o In elementary geometry, a polytope is a geometric object with flat sides, which exists in any general number of dimensions. A polygon is a polytope in two dimensions and a polyhedron in three dimensions.

Parts of the Polyhedra • 3 dimensions: The body is bounded by the faces, and is usually the volume enclosed by them.

Parts of the Polyhedra • 2 dimensions: A face is a polygon bounded by a circuit of edges, and usually including the flat (plane) region inside the boundary. These polygonal faces together make up the polyhedral surface.

Parts of the Polyhedra • 1 dimension: An edge joins one vertex to another and one face to another, and is usually a line segment. The edges together make up the polyhedral skeleton.

Parts of the Polyhedra • 0 dimensions: A vertex (plural vertices) is a corner point.

Where are polyhedrons found in everyday life?

There are many types of Polyhedra, more than we could possibly have time to look at!

What will we be doing with Polyhedra? • We are each going to make our own Polyhedra! o Each student will create a design which uses either pattern or rhythm to draw on the faces of a polyhedron. o Polyhedrons will either have 8+ faces, or the student will make 2 in order to reach the 8 face requirement.

How will we make them? • FIRST You will pick which shape you want from a template! =

How will we make them? • SECOND you will make 3 sketches of your pattern/rhythm design! Then pick the best one!

How will we make them? • THIRD you will take the template you want, and trace it on cardstock (thick) paper using the light table! • Use a ruler so that your edges are straight!!!!

How will we make them? • FOURTH you will draw your design using Prisma. Color Markers on your traced template! • DON’T CUT IT OUT YET!!!

How will we make them? • FIFTH: Once your design has neatly been applied to your template, it is time to cut it out! You can use scissors if you have a steady hand, but it would be best to use an X-acto knife with a metal straight edge.

How will we make them? • SIXTH step is to fold all of your edges! o If you use a tool to perforate the edges, it will make it easier to fold and look nicer.

How will we make them? • The LAST step is to glue the edges down. This is by far the HARDEST step, so work SLOWLY and CAREFULLY!!!!

How will we make them? • After you apply glue to one section, hold it for about a minute, assuring that it has adhered!

The final product should look something like these: