On bodies with congruent sections or projections

2017/11/28 by Ning Zhang, Zhang, Ning
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Mathematics and Applications #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1711.10445

openalex publication_date 2017/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we construct two convex bodies K and L in ℝⁿ, n≥ 3, such that their projections K|H, L|H onto every subspace H are congruent, but nevertheless, K and L do not coincide up to a translation or a reflection in the origin. This gives a negative answer to an old conjecture posed by Nakajima and Süss.

Related

• On bodies with directly congruent projections and sections
• On bodies in ℝ⁵ with directly congruent projections or sections
• SO(2)-congruent projections of convex bodies with rotation about the origin
• On polytopes with congruent projections or sections
• Counterexamples Related to Rotations of Shadows of Convex Bodies