¶ Allspace Filling: Self-Packing
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Index Entry
There are to my knowledge now six unique, all space filling geometries. Any one of them can be m amplified upon in unlimited degree by high frequency permitted aberrations. For instance,the cube can reoccur in high frequency multiples with fundamental m rectilinear aspects-- with a node on the positive face and a corresponding dimple on the negative face-- which will fill all space simply because it is a complex of cubes.
The six fundamental all space fillers are:
(1) The cube (six faces), discoverer unknown.
(2) The rhombic dodecahedron, discovererunknown (twelve faces). This all space filler is the one to occur most frequently in nature. Rhombic dodsecahedron crystals are frequently found on the floor of mineral rich deserts.
(3) Lord Kelvin’s tetrachideca (14 faces).
(4) Keith Critchlow’s snub-cornered tetrahedron (16 faces).
(5) My own-- Fuller’s asymmetric tetrahedron (4 faces).
(6) My own-- Fuller’s asymmetric hexahedron (six faces).
¶ Citations
- 4 May 1966 addendum to RBF letter to Steve Baer of 19 April 1966
