Activity 11 Five Intersecting Tetrahedra
Thomas Hull · 2006
This chapter presents an activity for students to learn how to make a modular origami tetrahedral frame using Francis Ow’s 60 degrees unit. The activity challenges the students, in groups, weave five such tetrahedra together to make an origami version of the compound of five tetrahedra. Making one tetrahedral frame is not hard. But weaving five together in the proper way is a big puzzle. To do so requires grappling with some unusual symmetries in three dimensions that are based on natural properties of the dodecahedron. The five tetrahedra model shares many symmetries with the dodecahedron. It has 120 degrees rotational symmetry about the axes connecting two opposite tetrahedron corners, 72 degrees rotational symmetry about the axes through points where five tetrahedra meet, and 180 degrees rotational symmetry about the axes through the “midpoint” between two nearby tetrahedron corners.