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This month’s challenge is inspired by Dungeons and Dragons and Stranger Things. D&D involves spinning dice, which are regular convex polyhedrons. The most common dice used are d4 (tetrahedron), d6 (cube), d8 (octahedron), d10 (decahedron), d12 (dodecahedron), and d20 (icosahedron), where ‘d’ is for die and the number indicates the number of sides. In this challenge, we will focus on the Platonic solids, which are the regular polyhedrons made up of regular polygons (the lengths of each side and interior angles are equal). In other words, skip the 10-sided die.
Most references define regular polyhedrons as a function of the edge length of one of the polygonal faces. In this challenge, we are defining the regular polyhedrons by the radius of the circle that circumscribes a polygonal face.
Your challenge is as follows:
As always, documentation is key! Someone should be able to read the worksheet and understand what problem you are trying to solve. Have fun!
Find the Mathcad Community Challenge Guidelines here!
Some additional links about polyhedrons and Platonic Solids that may be of interest:
https://www.cuemath.com/geometry/polyhedron/
https://www.varsitytutors.com/hotmath/hotmath_help/topics/platonic-solids
https://www.splashlearn.com/math-vocabulary/geometry/polyhedron
(The latter two can be share with your kids, as they are intended for a younger audience.)
Add r=1 plot.
Add resistances of 1 edge and most far points.
Ah, yay, more checkboxes!
Clicking the checkbox for painting in the plot is really fun.
Here's my limited attempt using Prime 8 Express.
Alan
My first Prime 10 Document. No plots!
No specific units used for the Length.
I thought I might need to check some of the math using a 3D CAD model, so here is an icosahedron modeled in Creo 7 if anyone else wants to do the same.