# Tag Archives: triangular

# An Icosahedron, Augmented with Twenty Triangular Cupolae, Together with Its Dual

After making the above polyhedron using *Stella 4d* (a program you can try for free at www.software3d.com/Stella.php), I checked its dual, which is shown below. I was surprised at its appearance, for it resembles a stellated polyhedron, even though it was created by a completely different process.

## Circumslices

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Regions between close-packed circles of equal radius resemble triangles, but with 60 degree arcs replacing the sides. As these regions are the only things left of a plane after all such circles are sliced out, and they each are outside all the circles used, I’ve decided to name them “circumslices.” Interestingly, the three interior angles of a circumslice each asymptotically approach zero degrees, as one approaches circumslice-vertices, which are also the points of contact of the circles.

Why did I name these things “circumslices?” Because they needed a name, that’s why!

## Compound of Four Triangular Prisms

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Software credit: see http://www.software3d.com/stella.php