I recently posted a question & answer to Mathematics StackExchange about an infinite family of self-dual polytopes I discovered - https://math.stackexchange.com/question ... -self-dual.

Having used polymake to research this topic, I provided the recommended polymake citations at the end. Also, I made use of homogenous coordinates, a la polymake, which simplified the presentation of the answer.

Each polytope defined in the Q&A is essentially a certain simplex placed on top of a hypercube. I show that these polytopes are self-dual by showing a facet-vertex incidence matrix for each which is symmetric. Interestingly, a Sierpinski triangle pattern forms in the NW quadrant of the incidence matrix.

The question is "on hold" at this writing, indicating that the site sponsors aren't ready to endorse it as a viable question. Answering your own question is an acceptable practice at MSE, although more commonly, users ask questions to get help and advice from mathematically sophisticated users. I encourage you to check it out!