Dissecting a Regular Tetrahedron into Four Congruent Pentahedra
The regular tetrahedron (a Platonic solid) can be dissected in multiple ways for a puzzle. In this project, a tetrahedron is sliced into four congruent pieces using two planes containing the midpoints of three edges (see figure below). Each piece is a pentahedron with two equilateral triangles, two right triangles, and a rhombus. You would need 4 copies for a tetrahedral puzzle.
This can be used as a entry project to learn about 3D sketching, extruding at a taper angle, etc. The Dihedral angle of a regular tetrahedron is arccos (1/3). Of course, we can also make a tetrahedron by slicing a cube. Have fun!
STEAM educator, learning from and working with K-12 STEAM teachers to explore new ideas of teaching and engagement. I firmly believe ART is at the core of STEM learning or all human learning! I owe my ideas and designs to the hundreds of K-12 children and teachers and university professors I have had the pleasure of working with, in multiple disciplines-- math, science,engineering language arts, social studies, early childhood education and more! All mistakes, of course, are mine! There is no warranty or liability whatsoever implied or explicit behind the designs or ideas. They are all posted for their potential educational values.
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