Draft:Equiprojective polyhedra

{{AfC submission|t||ts=20250405095658|u=Dedhert.Jr|ns=118|demo=}}

In mathematics, a convex polyhedron is defined to be $k$ -equiprojective if every orthogonal projection of the polygon onto a plane, in a direction not parallel to a face of the polyhedron, forms a $k$ -gon. For example, a cube is 6-equiprojective: every projection not parallel to a face forms a hexagon, More generally, every prism over a convex $k$ is $(k+2)$ -equiprojective.{{r|shephard|cfg}} Zonohedra are also equiprojective.{{r|buffiere}} Hasan and his colleagues later found more equiprojective polyhedra by truncating equally the tetrahedron and three other Johnson solids.{{r|hhl}}

{{harvtxt|Hasan|Lubiw|2008}} shows there is an $O(n \log n)$ time algorithm to determine whether a given polyhedron is equiprojective.{{r|hl}}

References

{{reflist|refs=

{{cite arXiv

| last = Buffière | first = Thèophile

| year = 2023

| title = Many equiprojective polytopes

| class = math.MG

| eprint = 2307.11366

}}

{{cite book

| last1 = Croft | first1 = Hallard

| last2 = Falconer | first2 = Kenneth

| last3 = Guy | first3 = Richard

| year = 1991

| title = Unsolved Problems in Geometry: Unsolved Problems in Intuitive Mathematics

| url = https://books.google.com/books?id=rdDTBwAAQBAJ&pg=PA60

| pages = 60

| doi = 10.1007/978-1-4612-0963-8

| isbn = 978-1-4612-0963-8

}}

{{cite arXiv

| title = Some New Equiprojective Polyhedra∗

| first1 = Masud | last1 = Hasan

| first2 = Mohammad Monoar | last2 = Hossain

| first3 = Alejandro | last3 = Lopez-Ortiz

| first4 = Sabrina | last4 = Nusrat

| first5 = Saad Altaful | last5 = Quader

| first6 = Nabila | last6 = Rahman

| year = 2010

| class = cs.CG | eprint = 1009.2252

}}

{{cite journal

| journal = Computational Geometry

| volume = 40 | issue = 2 | year = 2008 | pages = 148–155

| title = Equiprojective polyhedra

| last1 = Hasan | first1 = Masud Hasan

| last2 = Lubiw | first2 = Anna

| doi = 10.1016/j.comgeo.2007.05.002

}}

{{cite journal

| last = Shephard | first = G. C.

| title = Twenty Problems on Convex Polyhedra: Part I

| journal = The Mathematical Gazette

| volume = 52 | issue = 380 | year = 1968 | pages = 136–147

| doi = 10.2307/3612678

| jstor = 3612678

}} See Problem IX.

}}