Every triangle has an infinite sequence of sceptres. I call an
interlocking pair of equilateral triangles a *sceptre*. This theorem says
there is an infinite sequence of sceptres intimately associated with each triangle. I only show two
sceptres here for obvious reasons. As with the infinite
hexagon sequence theorem, move a **red** dot
to change the given triangle to an arbitrary one, and slide the **green**
dot along one side of the triangle to change the parameterization. See the
paper
for details, such as why the word "sceptre" works. See if you can spot the
regular hexagons (from the infinite sequence) in this diagram and determine the
relationship between them and the sceptres.

**Don't give up.
**This applet takes several minutes to load. It's worth
the wait.

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