Part 1: Polyhedral Perspectives

The Archimidean solids are solids whose faces are regular polygons (but not all the same) such that every vertex is symmetric with every other vertex.

## Problem 3Part A:
This figure shows a cube decomposed along the diagonal into
3 square pyramids
(the bottom square of the cube is the base of one pyramid, the square
face towards us is another base, and the square face on the right side is
the third),
which would explain why the
volume of a square pyramid is one-third the height times the base.
Are they congruent pyramids though?
To answer this question, use this pyramid net. Make 3 copies. Do they fit together along the diagonal? |

Net for a right triangular prism

Part 2: Metric Perspectives (Taxicab and Euclidean)

For the following problems, you may do by-hand work and/or use Sketchpad.