Geometry Working Group
Tuesday, July 16
Geometry Workgroup, 3D Puzzle Subgrouop (JF, KK, BH)
Derivation of r.d. from the cube
Why are pairs of faces coplanar? I.e., why do the triangles actually form rhombi?
Determine dimensions (lengths of edges, face diagonals, "space diagonals") of the cube and then of the r.d.
Determine volume of the r.d. and relate to the cube
What polygons are the intersections of the r.d. and planes?
Which Platonic solids can be inscribed in the r.d.?
What is the dual of the r.d.?
(Advanced) One can fill space with r.d.s. Then the intersection with a plane will give a tiling of the plane, a la Philips course. What tilings arise this way?
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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.