Original scientific paper

https://doi.org/10.31896/k.29.1

Stellae Octangulae in Motion Revisited

Hellmuth Stachel ; Vienna University of Technology, Vienna, Austria *
Gunter Weiss ; Vienna University of Technology, Vienna, Austria

* Corresponding author.

Abstract

It is well-known that two congruent regular tetrahedra T_1 and T_2 forming a Stella Octangula allow a continuous motion of T_2 relative to T_1 such that each edge of T_2 slides along an edge of T_1. Recently the same property has been confirmed for pairs (T_1,T_2) of indirect congruent tetrahedra of general form. It turns out that this overconstrained kinematical systems admits besides some special one-parameter motions also two-parameter motions. We provide a synthetic analysis of the problem. Based on involved quadrics, we study in depth the two -parameter motions and their boundaries. Moreover, we present some generalizations of Stellae Octangulae.

Keywords

tetrahedron; Stella Octangula; Euclidean motion; two-parameter movements

Hrčak ID:

341355

URI

https://hrcak.srce.hr/341355

Publication date:

19.12.2025.

Article data in other languages: croatian

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