KoG, Vol. 29 No. 29, 2025.
Izvorni znanstveni članak
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
* Dopisni autor.
Sažetak
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.
Ključne riječi
tetrahedron; Stella Octangula; Euclidean motion; two-parameter movements
Hrčak ID:
341355
URI
Datum izdavanja:
19.12.2025.
Posjeta: 854 *