An Amazing, Space Filling, Non-regular Tetrahedron: As Simple as √1, √2, √3

Abstract

Exploring the shapes in this paper can increase student understanding of basic concepts of space geometry and allow teachers and students to consider ideas such as these:

• How can cubes be examined and used to create other examples of polyhedra that fill space?
• How can relationships from plane geometry such as the Pythagorean theorem, be used to find lengths and shapes to create nets to build space-filling polyhedra?
• How can models of these space-filling shapes be constructed and used to build intriguing, hinged 3-dimensional puzzles?