MA341 HOMEWORK #4
Due Friday, October 8

In each of the following problems, include a carefully drawn diagram and clearly labeled points, so that it is perfectly clear which points have which coordinates.

1. Determine the coordinates and the edge length of a cube centered at the origin so that each edge is parallel to one of the coordinate axes and such that one of the vertices (corners) has coordinates (1,1,1).
2. Determine the coordinates and the edge length of an octahedron centered at the origin so that each vertex is on one of the coordinate axes and such that one of the vertices has coordinates (1,0,0).
3. Determine the coordinates and the edge length of a truncated cube, where the vertices of the cube in the first problem are truncated so that each square of the original cube becomes a regular octagon.
4. Determine the coordinates and the edge length of a truncated octahedron, where the vertices of the octahedron in the second problem are truncated so that each equilateral triangle of the octahedron becomes a regular hexagon.

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