Using Power Polygons Or by Drawing Your Own Regular Polygons Explore Some of the Following

Polygons!

Using power polygons or by drawing your own regular polygons explore some of the following ideas:

 Lines of Symmetry: Determine the number of lines of symmetry for various polygons. Can you make a connection between the number of lines of symmetry and the polygon? What patterns, if any, do you notice?

 Combining polygons to make new polygons: Choose two congruent polygons and explore all the other polygons you can make by combining them. Compare regular and non-regular polygons.

 Combining many pieces to make a regular polygon: Using congruent pieces try to build other regular polygons such as a hexagon. Can you do this in more than one way? Try making other regular polygons?

 Combining non-congruent pieces: try making other polygons from two or more non-congruent polygons.

Record your findings and be prepared to share your discoveries! Platonic Solids!

Use the G-O Frames to build each of the platonic solids.

Explore the number of faces, edges, and vertices of each. Is there a connection between these three numbers for each platonic solid?

Explore the possible (and impossible) nets for each of these solids.

Record your discoveries and be prepared to share! Archimedean Solids!

Use the G-O Frames or Geo D-Stix to build some of the Archimedean Solids.

Use Schlafli notation to describe your polyhedrons.

Explore the number of faces, edges, and vertices. Is there a connection?

Explore the nets of the polyhedrons. Tessellations!

A tessellation is a tiling pattern that covers a plane with no overlaps or gaps. A regular tessellation is made using only one type of congruent polygon. A semi-regular tessellation is made using two or more regular polygons where the arrangement of polygons is the same at every vertex.

Using power polygons, pattern blocks, or your own hand- drawn polygons:  determine which polygons will tessellate a plane (create a regular tessellation)  find combinations of polygons that can create a semi-regular tessellation Record your results and be prepared to share!

Read the photocopied piece about “Schlafli Notation” for tessellations and try to describe your tessellations using this notation.

Extension:

Explore the information on pages 407 – 425 about tessellations and try to make your own tessellation picture.