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Algebraic degrees of 3-dimensional polytopes

Belotti, Mara; Joswig, Michael; Panizzut, Marta

Results of Koebe (Ber. Sächs. Akad. Wiss. Leipzig, Math.-phys. Kl. 88, 141–164, 1936), Schramm (Invent. Math. 107(3), 543560, 1992), and Springborn (Math. Z. 249, 513–517, 2005) yield realizations of 3-polytopes with edges tangent to the unit sphere. Here we study the algebraic degrees of such realizations. This initiates the research on constrained realization spaces of polytopes.
Published in: Vietnam Journal of Mathematics, 10.1007/s10013-022-00559-2, Springer Nature