#I built one of those twenty-sided bastards out of dowels and Krazy glue

[inspired-lesson-plans]

Do Now: (5 min+)

Stare deeply into the regular 4-dimensional polytope below until you become unanchored from linear time.

Guided Learning: (20 min)

Mathematics is fundamentally the art of the abstract. If I have 5 apples and you take away 3 apples, I am not left with 2 apples because no apples are identical and no real-world measurement can ever be infinitely precise. This is particularly evident in the practice of geometry. Call on students to explain the definitions of a familiar rank-2 polytope (triangle). After ensuring that have the correct definition (3 straight line segments that form 3 vertices), ask them what a triangle would look like in the real world. Encourage your students to prove that abstract shapes can only exist as abstract concepts.

Higher Order Learning: (remaining time)

Students work individually or in partner groups to browse the Convex Uniform Polyhedra and pick one to research. You should have a Google Slides file prepared on Google Classroom with each of the polyhedra as their own slide for the students to fill out. Don't just include basic information! There are plenty of opportunities for students to be creative in what they report! Give them time to read through the whole article! Keep them on-task and you'll be amazed at what they teach themselves!

I love the lists of regular polyhedra on Wikipedia

behold, the deltoidal hexecontahedron:

the great rhobihexahedron:

here we have the ditrigonal dodecicosidodecahedron:

the great retrosnub icosidodecahedron:

the beautiful twins, the sixteenth stellation of the icosidodecahedron, and her sister, the seventeenth stellation of same:

they look like some kind of mysterious and terrible Pokemon to me.

and lastly, her royal majesty, the final stellation of the icosahedron:

once when i was a child, i had a terrible earache that afflicted my dreams with nightmares of acute geometry. i think i saw her there, bloody and majestic, hovering above my bed.