Platonic Solids

So What is Our Topic?  It’s math (go figure!)  It’s hands on (so you get to play!)  There’s candy involved  There are some objects we will describe that are named after a famous person because everything has to be named something, right??  You know how this goes—here’s some real life examples of what I mean

Air Jordans

Tigerade

Platonic Solids

What are these Platonic Solids?  Regular three dimensional solids called polyhedra (because they are made from polygons)  All the faces (sides) are regular polygons  All the vertices (corners) look exactly the same  Convex  There are only five

px?id=70 px?id=70

Some definitions—so we all know what we’re talking about! Polygon- any figure that is closed (connected to itself) and has three or more sides that are straight, not curved Plural is polygons Plural is polygons These are flat (two dimensional) These are flat (two dimensional) Examples of polygons Examples of figures that are not polygons

Some definitions—so we all know what we’re talking about! Regular Polygon - a polygon has the same side lengths and same angle measures Examples of regular polygons Examples of figures that are not regular polygons

Some definitions—so we all know what we’re talking about! Polyhedron- a solid figure made up of polygons Plural is polyhedra Plural is polyhedra These are not flat (three dimensional) These are not flat (three dimensional) Would the polyhedra above ALL be considered regular?

Some definitions—so we all know what we’re talking about! Convex- a shape where the surfaces bulge outwards The opposite of this is concave The opposite of this is concave Examples of concave figures Examples of convex figures

Some definitions—so we all know what we’re talking about! Vertex- where three or more faces meet Plural is vertices Plural is vertices Hint—it’s the corners Hint—it’s the corners Face- the side Edge- where two faces (sides) meet Forms a line segment Forms a line segment

Euler’s Formula--Cool Rule! Faces + Vertices - Edges = 2 This is true for all convex polyhedra Not just true for platonic solids 1752

What is a Net?  If you had a 3D shape made out of paper, that was all folded and taped together, and you pulled the tape off and laid the figure out flat, then you would get the net of the three dimensional solid.  There’s more than one net for each solid.

 +in+geometry&page=1&qsrc=19&ab=2&u =http%3A%2F%2Fwww.mathsnet.net%2F geometry%2Fsolid%2Fnets.html +in+geometry&page=1&qsrc=19&ab=2&u =http%3A%2F%2Fwww.mathsnet.net%2F geometry%2Fsolid%2Fnets.html +in+geometry&page=1&qsrc=19&ab=2&u =http%3A%2F%2Fwww.mathsnet.net%2F geometry%2Fsolid%2Fnets.html

Your turn  Using the plastic squares and triangles  Make as many nets as possible for a cube and tetrahedron  Draw ALL of your nets on the grid paper  Hint---there are eleven for the cube and two for the tetrahedron!!  First one to get all eleven for the cube gets a candy bar  Duplicates don’t count!

No duplicates!

Let’s look at the nets x?ID=84 x?ID=84 es/nets/netscube+puzzle.pdf es/nets/netscube+puzzle.pdf