914.00 A Quanta Module: Foldability

914.01 The A Quanta Module can be unfolded into a planar triangle, an asymmetrical triangle with three different edge sizes, yet with the rare property of folding up into a whole irregular tetrahedron.

914.02 An equilateral planar triangle /// may be bisected in each edge by points BBB. The triangle AAA may be folded on lines BB, BB, BB, and points A, A, A will coincide to form the regular tetrahedron. This is very well known.

914.10 Four Right Angles: In respect to the / Quanta Module flatout triangle or infolded to form the irregular tetrahedron, we find by the method of the module’s construction (by perpendicular planes carving apart) that there are four right angles (see Illus. 913.01C):

EFB EDC

EFC ADC

914.20 Unfolding into a Flat Triangle: If we go to the vertex at# and break open the edges ED and AD, we can hinge open triangle EBF on hinge lineEF. We can then break open the edge/C and fold triangle ADC, as well as folding out the two triangles DEC and CEF, which are connected by the hinge EC, so that now the whole asymmetric / Quanta Module is stretched out flat as a triangle.

914.21 The A Quanta Module unfolds into a scalene triangle; that is, all of its non-90-degree angles are different, and all are less than 90 degrees. Two of the folds are perpendicular to the triangle’s sides, thus producing the four right angles. The/ Quanta Module triangle may be the only triangle fulfilling all the above stated conditions.

914.30 Spiral Foldability: The foldability of the A Quanta Module planar triangle differs from the inter-mid-edge foldability of the equilateral or isosceles triangle. All the mid-edge-foldable equilateral or isosceles triangles can all form tetrahedra, regular or irregular. In the case of the folded equilateral or isosceles triangle, the three triangle corners meet together at one vertex: like petals of a flower. In the case of the inter-mid-edge-folding scalene triangle, the three corners fail to meet at one vertex to form a tetrahedron.