All Title Author
Keywords Abstract

Publish in OALib Journal
ISSN: 2333-9721
APC: Only $99

ViewsDownloads

Relative Articles

More...
Algorithms  2012 

Imaginary Cubes and Their Puzzles

DOI: 10.3390/a5020273

Keywords: imaginary cubes, hexagonal bipyramid, triangular antiprismoid, assembly puzzles, 3D tessellation

Full-Text   Cite this paper   Add to My Lib

Abstract:

Imaginary cubes are three dimensional objects which have square silhouette projections in three orthogonal ways just as a cube has. In this paper, we study imaginary cubes and present assembly puzzles based on them. We show that there are 16 equivalence classes of minimal convex imaginary cubes, among whose representatives are a hexagonal bipyramid imaginary cube and a triangular antiprism imaginary cube. Our main puzzle is to put three of the former and six of the latter pieces into a cube-box with an edge length of twice the size of the original cube. Solutions of this puzzle are based on remarkable properties of these two imaginary cubes, in particular, the possibility of tiling 3D Euclidean space.

Full-Text

comments powered by Disqus

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133

WeChat 1538708413