Families of Four-Point Touching Equilateral Triangles

This Demonstration shows four-point touching families of equilateral triangles, where , .
The parameter , where is the smaller diagonal of the rhombus.

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A family is said to be -touching provided each element of has a nonempty intersection with precisely other elements of . A -touching family is said to be point- touching if any two touching sets have only a single common point [1].
[1] B. Grünbaum, "Families of Point-Touching Squares," Geombinatorics, 12(4), 2003 pp. 167–174. (Mar 27, 2019) sites.math.washington.edu/~grunbaum/Familiesofpointtouchin.pdf.
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