Pith. sign in

REVIEW 2 cited by

Flexible polyhedral nets in isotropic geometry

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2504.15060 v1 pith:LG45CB76 submitted 2025-04-21 math.MG

classification math.MG
keywords geometrynetsflexiblepolyhedralclasseseuclideanflexibilityisotropic
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

We study flexible polyhedral nets in isotropic geometry. This geometry has a degenerate metric, but there is a natural notion of flexibility. We study infinitesimal and finite flexibility, and classify all finitely flexible polyhedral nets of arbitrary size. We show that there are just two classes, in contrast to Izmestiev's rather involved classification in Euclidean geometry, for size 3x3 only. Using these nets to initialize the optimization algorithms, we turn them into approximate Euclidean mechanisms. We also explore the smooth versions of these classes.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Quasi-symmetric nets: A constructive approach to the equimodular elliptic type of Kokotsakis polyhedra

    math.MG 2025-11 conditional novelty 7.0 of 10

    Quasi-symmetric nets are introduced and shown to be flexible realizations of the equimodular elliptic type of Kokotsakis polyhedra, with closed-form and numerical examples.

  2. Unlocking Euclidean Problems with Isotropic Initialization

    cs.CG 2025-06 conditional novelty 7.0 of 10

    A two-step method, solve in isotropic geometry then optimize to Euclidean, constructs flexible quad meshes, asymptotic-geodesic webs, and constant-angle asymptotic gridshells.

Pith tools