Polyhedra – arbitrarilyclose

#MathArtChallenge 100: Balloon Polyhedra

In the first, allow me to thank each and every one of you who has participated in the #MathArtChallenge in the last few months. This is my “last” post. Meaning, I don’t promise to make more Math Art Challenges, but there’s always the chance that something will come up…

All of the #MathArtChallenge-s will continue to be up on this blog, and I really hope that you’ll make use of them in your classes or in your fun time or however brings you joy.

The Challenge: Today, you get Balloon Polyhedra. There’s actually several papers written about this, so go check them out.

Materials needed: Twisting balloons, pump, patience
Math concepts you could explore with this challenge: angles, arithmetics, counting, geometry, graph theory, polygons, polyhedra, symmetry, vertices/intersections

#MathArtChallenge 97: Tomoko Fusé’s Bird Tetrahedron Origami

The Challenge: Make an origami sculpture using Tomoko Fusé’s text Multidimensional Transoformations Unit Orgiami. (I used instructions on pgs 134, 138-139.)

Materials Needed: Paper (origami paper is handy, but any paper will work) and scissors/paper cutter.
Math Concepts: 3 dimensional building, angles, space filling, rotations, proportions

#MathArtChallenge 93: Archimedean Solids from Vertex descriptions

The Challenge: Using a vertex description, build yourself one, two… up to all 13 of the Archimedean solids.

Materials needed: Card stock and tape (painter’s tape is great, or masking. Other stuff will work, but I’ve had more success with the paper-y tapes.) OR Magnatiles, but those can get pretty pricey.
Math Concepts: structure, polyhedra, angles, 3D structure

#MathArtChallenge 91: 3D Cube Cut-Outs

A potato cut in the shape of a letter A, with shadow behind it.

The Challenge: Find some materials that will allow you to create one of those beautiful 3D 3-letter (or shape? Follow your heart) cut-outs. I used a potato.

Materials Needed: Something you can cut up. Potatoes, crafting foam, apples… food, I think would work well here.
Math concepts you could explore with this challenge: angles, geometry, perspective, polyhedra, symmetry

#MathArtChallenge 87: Burr Puzzle Origami

An origami stellated polyhedra made from origami

The Challenge: Fold yourself a 6 piece puzzle that comes together as a 3D star shape. You’ll need 6 pieces of paper.

Materials Needed: 6 square pieces of paper.
Math concepts you could explore with this challenge: angles, geometry, origami, polygons, polyhedra, vertices.

#MathArtChallenge Day 39: Flowered Dodecahedron

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 concepts you could explore with this challenge: geometric construction, geometry, polygons, polyhedra, symmetry, vertices/intersections

#MathArtChallenge Day 29: Paper Roll Polyhedra

2020-04-12 14.40.31 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

For my 8000th tweet, here’s how to make a truncated icosahedron from toilet roll tubes.👇 pic.twitter.com/WCdpJaRbey
— Mr Allan (@mrallanmaths) May 6, 2019

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

#MathArtChallenge Day 27: Golden Icosahedron

The Challenge: Create your very own Golden Rectangle Icosahedron!

Materials Needed: Cardboard, markers, scissors/box cutter, string/ribbon/thread
Math concepts you could explore with this challenge: angles, geometric construction, geometry polygons, polyhedra, proportions/ratios, vertices/intersections

#MathArtChallenge Day 20: Origami Icosahedron

Day20 Icosahedron — A spinning icosahedron made from origami paper.

The Challenge: Fold 30 identical pieces of paper to put together as an icosahedron.

Materials Needed: 30 square pieces of paper. No problem if it’s not origami paper, you can use regular paper (and you can decorate it if you want!)
Math concepts you could explore with this challenge: Geometry, graph theory, origami, polygons, polyhedra, symmetry, vertices/intersections

#MathArtChallenge Day 17: PERMUTOHEDRONS

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 concepts you could explore with this challenge: angles, combinations & permutations, geometric construction, geometry, graph theory, polyhedra, sequences, vertices/intersections.