a2.5.0 (feature) - Duoprisms

• Added a FixedDuoPrism scene.

This scene includes two sliders, both of which representing two different polygons with different amount of sides respectively. The sliders range from 2 (line segment, technically not a polygon) to 8 (regular octagon).

The Cartesian product of the vertices of these two polygons get taken to create a Duoprism. In other words, if you take every point of polygon A as (x, y) and for each of these points take all points of polygon B as (z, w) and connect the points, you get the (wireframe) of a Duoprism.

If you have either of the sliders at the minimum, you will get what looks like a normal prism; however dragging the other slider will quickly increase the object’s complexity. If the sliders are set to 4-4, you will notice that you get a tesseract, which is the cartesian product of two squares. The more both sliders are increased the more you may notice it looks more and more like the object in the FixedCliffordTorusHyperscene - this is not a coincidence. Since polygons with an increasing amount of vertices approach a circle, duoprisms with higher vertex counts approach something that is called a Duocylinder.

It’s important to clarify the difference between a Duocylinder and a Clifford torus, as the Clifford torus is just a 2D manifold of the “ridge” (the boundary between the two solid torus cells) of the Duoprism.