Orthodiagonal anti-involutive Kokotsakis polyhedra

Ivan Erofeev, Grigory Ivanov

Research output: Contribution to journalArticlepeer-review


We study the properties of Kokotsakis polyhedra of orthodiagonal anti-involutive type. Stachel conjectured that a certain resultant connected to a polynomial system describing flexion of a Kokotsakis polyhedron must be reducible. Izmestiev [3] showed that a polyhedron of the orthodiagonal anti-involutive type is the only possible candidate to disprove Stachel’s conjecture. We show that the corresponding resultant is reducible, thereby confirming the conjecture. We do it in two ways: by factorization of the corresponding resultant and providing a simple geometric proof. We describe the space of parameters for which such a polyhedron exists and show that this space is non-empty. We show that a Kokotsakis polyhedron of orthodiagonal anti-involutive type is flexible and give explicit parametrizations in elementary functions and in elliptic functions of its flexion.
Original languageEnglish
Article number103713
JournalMechanism and Machine Theory
Early online date26 Dec 2019
Publication statusPublished - 1 Apr 2020


  • Kokotsakis polyhedron
  • Spherical linkage
  • Stachel's conjecture
  • flexible polyhedron


Dive into the research topics of 'Orthodiagonal anti-involutive Kokotsakis polyhedra'. Together they form a unique fingerprint.

Cite this