The Challenge: Fold you own octahedron from 6 square pieces of paper.

Materials Needed: 6 square pieces of paper. Math conceptsyou could explore with this challenge: angles, geometric construction, geometry, origami, symmetry, vertices/intersections

Materials Needed: Compass, increasingly large circles to trace or graphing technology. Math conceptsyou could explore with this challenge: Circles, geometric construction, geometry, symmetry, vertices/intersections

The Challenge: Suggested by Clarissa Grandi, to cut out and construct this flowered dodecahedron. Mine below followed by links to instructions. Materials Needed: A set of these papers printed and cut from cardstock. (there are other sized pieces available at the links below. Math conceptsyou could explore with this challenge: geometric construction, geometry, polygons, polyhedra, symmetry, vertices/intersections

Materials Needed: In an ideal world, you have a compass and ruler, but sans compass, you just need to do your best to divide a circle into 10 equal pieces. Math conceptsyou could explore with this challenge: angles, geometric construction, geometry, islamic geometry, lines, vertices/intersections

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

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

The Challenge: Find a smaller circle you can trace. Then trace large circle to use as a guide. Finally, trace a bunch of smaller circles in a ring to create a torus (more commonly known as a donut).

Materials Needed: Paper, writing utensil(s), circles/compass. The circles can be whatever, but rigid is helpful and even better if they’re empty (masking tape is great!) Math conceptsyou could explore with this challenge: circles, geometric construction, proportions/ratios (to get interlocking tori, there are restrictions on the possible ratios between the circles)