The cube is the only platonic solid that can fill space, although a tiling that combines tetrahedra and octahedra (the tetrahedral-octahedral honeycomb) is possible. Although the regular tetrahedron cannot fill space, other tetrahedra can, including the Goursat tetrahedra derived from the cube, and the Hill tetrahedra.
There exist precisely 914, 58, and 46 equivariant types of tile-transitive tilings of three-dimensional euclidean space by topological cubes, octahedra, an.
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Aug 5, 1997 · Tiling Space By Platonic Solids I. Olaf Delgado Friedrichs. Daniel H. Huson. August 5, 1997. Abstract. There exist precisely 914, 58 and 46 ...
We discuss this question in a series of two papers. In this, the first paper, we state that there exist precisely 914, 58 and 46 equivariant types of ...
Oct 1, 2017 · To be specific, we're talking about an affine-regular tiling of a hyperboloid here (what this author calls a “hyperbolohedron”). With polygonal ...
This paper examines a range of geometric concepts of importance to the further understanding of two-and three-dimensional design.
Dec 21, 2020 · Is it possible to tile dodecahedrons in a 3D grid without any spaces between them? Feel free to send me web links about that. platonic-solids.
There exist precisely 914, 58, and 46 equivariant types of tile-transitive tilings of three-dimensional euclidean space by topological cubes, octahedra, ...
Oct 2, 2023 · How do you pack dodecahedra? The cube is the only Platonic solid which fills 3-dimensional space. A little research found me this: mathworld.
Tiling Space by Platonic Solids, I. Friedrichs, O.D.; Huson, D.H.. Discrete and Computational Geometry 21(2): 299-315. 1999. ISSN/ISBN: 0179-5376. DOI: 10.1007 ...