And now is a great time to explore some polyhedra if you haven’t yet done so! Here are some websites shared by Mark Kaercher that are great.

The Challenge: Make your very own paper roll polyhedra. All inspired by this tweet from Mr. Allan shared by Clarissa Grandi

Materials Needed: Paper rolls. Can be toilet paper or paper towel rolls or you can make your own! Math conceptsyou could explore with this challenge: angles, geometry, polygons, polyhedra, symmetry, vertices/intersections

The Challenge: Today, courtesy of the extraordinary Mark Kaercher:

Materials Needed: Cardboard tube (toilet paper or paper towel rolls) Math conceptsyou could explore with this challenge: angles, geometry, polygons, symmetry

The Challenge: Great your very own tessellation from a small piece of cardboard.

Start with a square (Cereal or pop box cardboard works great) Mine was 2”x2”

Cut a piece from one side and tape it to an adjacent side.

Repeat for remaining 2 edges.

Trace!

Materials Needed: Pencil, paper, and cardboard from a cereal box or a pop box or something similarly thin but stiff enough to trace. Math conceptsyou could explore with this challenge: angles, geometry, polygons, tessellations, vertices/intersections

4 polygons with multiple iterations of midpoints connected inside the shape.

The Challenge: Draw a polygon. Then mark the midpoint of each side. Connect the midpoints of each side to make a new polygon. Repeat. (Don’t sleep on the quadrilaterals here. They do something rather surprising and beautiful!)

Materials Needed: Paper & pencil or online graphing software like Geogebra or Desmos Math conceptsyou could explore with this challenge: angles, fractals, functions, geometry, lines, polygons, proportions/ratios, slope symmetry, vertices/intersections.

A green lattice design with clearly visible pencil marks from a compass behind them.

The Challenge : Create this design from the Agra Fort.

Materials Needed: If you have a compass, use this tutorial from Samira Mian. If you do not have a compass, you can use my instructions for making this from a regular grid below that. Math conceptsyou could explore with this challenge: angles, geometric construction, lines, polygons, symmetry, tesselations, vertices/intersections

The Challenge: Create your very own order 4 Permutohedron (see video below).

Materials Needed: Paper, pencil, patience, and if you want to go 3D, you sure can. Post-it notes work pretty well when playing with this. Math conceptsyou could explore with this challenge: angles, combinations & permutations, geometric construction, geometry, graph theory, polyhedra, sequences, vertices/intersections.

The Challenge: Create an illusion using isometric lines.

Materials Needed: Isometric Grid paper You can print some or you can create some (that just takes a bit of patience), pencil and ERASER. This challenge is best done as an exercise in erasing, changing and play. You can see in my time lapse below just how much erasing I did and I’ve done this kind of thing many times before. Be gentle with yourself. Math conceptsyou could explore with this challenge: Angles, geometric construction, geometry, isometric grids, perspective

Construction (compass and straight edge) of a tessellation of 8 pointed stars.

Note: This is a first foray for the #mathartchallenge into Islamic Geometry. I would be a fool to not take this opportunity to teach you about Samira Mian. Her online courses are fantastic, and her tutorials are great. So are is her instagram!

The Challenge: Construct an 8-pointed star, and possibly tile it?

Materials needed: Straight edge, writing utensils, paper, compass? (There are tutorials for both compass and no compasses below.) Math conceptsyou could explore with this challenge: angles, circles, geometric construction, Islamic geometry, symmetry, tessellations, vertices/intersections