Geometry Working Group

Tuesday, July 16

Geometry Workgroup, 3D Puzzle Subgrouop (JF, KK, BH)

an augmented cube, the neglected polyhedron:

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 Philip’s course. What tilings arise this way?

Back to Journal Index

PCMI@MathForum Home || IAS/PCMI Home

© 2001 - 2016 Park City Mathematics Institute
IAS/Park City Mathematics Institute is an outreach program of the Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540
Send questions or comments to: Suzanne Alejandre and Jim King

With program support provided by Math for America

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.