Some New Equiprojective Polyhedra

TL;DR

This paper introduces new classes of equiprojective polyhedra by applying cutting and gluing techniques, advancing the understanding of their geometric properties and classification.

Contribution

It presents novel equiprojective polyhedra constructed through innovative geometric operations, building on Hasan and Lubiw's characterization.

Findings

Discovered new equiprojective polyhedra via cutting and gluing

Extended the classification of equiprojective polyhedra

Provided geometric constructions for previously unknown shapes

Abstract

A convex polyhedron $P$ is $k$-equiprojective if all of its orthogonal projections, i.e., shadows, except those parallel to the faces of $P$ are $k$-gon for some fixed value of $k$. Since 1968, it is an open problem to construct all equiprojective polyhedra. Recently, Hasan and Lubiw [CGTA 40(2):148-155, 2008] have given a characterization of equiprojective polyhedra. Based on their characterization, in this paper we discover some new equiprojective polyhedra by cutting and gluing existing polyhedra.