Third level tetraflexagon

The generic third level tetraflexagon has thirty six faces, and is still easy to fold up from a previously prepared strip of paper. However, rather than many pages of explicitly numbered squares, the templates described in the next section should be consulted.

The easiest way to create a generic flexagon is to prepare some uncolored and unnumbered segments corresponding to the sign sequence $(+ + + + \cdots)$ with tabs on the end. They can later be joined and labelled as required. It is especially easy with triflexagons because a long straight strip of paper only has to be marked off into triangles. Polygons with more sides still use an essentially straight strip of paper, but with little meanders which have to be incorporated since the beginning.

  

Figure 36: Since each of the twelve edges of the second level tetraflexagon spawns two new vertices, the full second level tetraflexagon has 36.

+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+
1	3	3	17	17	19	13	15	15	11	11	13	25	27	27	23	23	25	19	21	21	35	35	37	31	33	33	29	29	31	7	9	9	5	5	7	1
2	2	4	16	18	18	14	14	16	10	12	12	26	26	28	22	24	24	20	20	22	34	36	36	32	32	34	28	30	30	8	8	10	4	6	6	2

  

Figure 37: Permutation of the squares along the strip for a third level tetraflexagon.

November 1, 2000