The DICTO Hexa: a cube of 8 DICTO Hexa Jewels, the Hexa-Key, and their 5 : 3 checkerboard filling of space
Year: 2026
Type: preprint
Abstract: The DICTO Jewel is the regular dodecahedron of the Euclid–Kepler–Pacioli cell carved by the stella octangulas of its six neighbouring cells (volume 12 at cube edge 2); with stella octangulas it fills space. Eight DICTO Hexa Jewels (exact DICTO Jewels on a 2 × 2 × 2 block of cells, unsheared and passing through each other inside) form one solid, the DICTO Hexa: a cube of edge 4 with 24 outward roofs on its faces, volume 80 (6⅔ Jewels). No shear makes eight Jewels meet face to face as a cube; the Hexa exists only as overlapping exact Jewels. Hexas mate only window to window; at the FCC pattern of spacing 4 each has 12 neighbours, and the space between them is one solid, the DICTO Hexa-Key (8 stella octangulas and 12 double roofs, volume 48). Hexas and Hexa-Keys fill space as a checkerboard, 5 : 3 by volume, the Stella–Jewel Lattice one level up. The Hexa splits exactly into 8 cubes and 24 roofs, or into 4 whole and 4 trimmed Jewels. Clusters of eight Hexas, a diamond network of Hexas and stellas, and the absence of any turning join are also given. Not found in a web search (2026-10-09) or in our reference library (2026-10-15). First released inside Kaleidohedra v2026.10.11-octet (DICTO DOI: 10.5281/zenodo.23284390); this is its own record. Data, renders and the check outputs are included. Computation and checking with Claude (Anthropic) in the open-source library krp-core (v0.16.0). Explore it in the apps: https://dictospheres.com
Author: DICTO
Institution: Independent Dance
Language: English
Subfield: Visual Arts and Performing Arts
Field: Arts and Humanities
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7221828962
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