KALEIDOHEDRA by DICTO
In development — live at kaleidohedra.dictospheres.com, rhombiverse.dictospheres.com and polyhedraverse.dictospheres.com. Since 2026-10-08 this repository is one app with two front doors: Kaleidohedra (orange), lattices you can shear and slide continuously, every piece moving with the lattice, and Rhombiverse (cyan), lattices of space-filling shapes from 1D to 6D. Each door has its own address, welcome, colours, guide and saved worlds; behind them the worlds, typography and controls are shared. The DICTO menu (top left) opens on the app you came in by, with the others a button away. Polyhedraverse (green), the portrait gallery of 333 polyhedra and the six regular 4D polytopes, now lives here too (step D, 2026-10-09): its space, shape browser, nets, 4D builds and hints are in both doors' DICTO menu, and since 2026-10-10 it has its own third door here, polyhedraverse.dictospheres.com (SITE=polyhedraverse); the old Polyhedraverse repository is archived (KRP, DICTO's plan for the three). The geometry all three share is krp-core.
- Per-app content (head, changelog, icons):
site/<app>/; the one DICTO User Guide (shared sections, a chapter per app, 7 languages): site/guide/. The apps' table (names, colours, which tools each has): src/app/site.js; one type scale for all: src/app/tokens.css.
- Building a front door:
SITE=kaleidohedra npm run build or SITE=rhombiverse npm run build (each Vercel project sets its own). Locally, index.html?site=rhombiverse opens Rhombiverse's door.
- Generalized Permutohedra (DICTO → 3D+, Kaleidohedra's worlds): the 3D permutohedron's deformation cone (Postnikov 2009), every shape it becomes when its faces slide without tilting; one slider to Loday's associahedron, one face at a time, with a wall marked at each face's vanishing, stops at the simplex, cube, hypersimplex, cyclohedron, associahedron and permutohedron, and a live fills-space badge (Venkov–McMullen).
?open=gperm.
- DICTO's newest worlds (DICTO → 3D+, each from his ideas and papers, with its DICTO DOI in the Almanac): Every Mix of the Platonic Solids (#47), The Reuleaux Platonic Solids (#45), Aristotle's Pyramid (#44), The OG on the Octet Truss (#37) and Universal PiTet (#38) with its cycle film and The Kepler–Poinsot–UP Cycle; in Studies, the DICTO stretched solids (#49, The Polyhedral Stretching Theorem), opened directly by kaleidohedra.dictospheres.com/?open=studies:stretch. Polyhedraverse's newest family is the Mosseri–Sadoc tiles (1982): the six golden tetrahedra of Mosseri and Sadoc, among them DICTO's Hound Tooth, Tricap, Cleo and AXE.
Polyhedraverse's families include DICTO's Reuleaux Platonic Solids (paper #45, DICTO DOI 10.5281/zenodo.23529499), the five curved bodies of Kaleidohedra's Reuleaux world, drawn smooth and fitted by their corners (one body data in krp-core serves both). On all three doors the Soft view (the puffed-square button in the tools column) shows any build with every flat face bulged into a soft cap, in a Plain, Metallic or Ceramic finish; it is a view only, the real pieces stay underneath for tapping and snapping (krp-core puffed.js, src/app/soft-finish.js). Polyhedraverse's ◌ DICTO Vacuus lens (2026-11-03) sees any solid whose centre lies inside all its face planes from that centre, in five views: Pyramids, Exploded, Star, Sheets (fins coloured by congruence) and Struts (coloured by length), opened directly by polyhedraverse.dictospheres.com/?open=vacuus:CUBE; Aristotle's Pyramid links to it and back (src/app/vacuus-geometry.js, src/app/vacuus-lens.js). Its ✂ Golden Cut (paper #88) cuts any of the five Platonic solids the same depth at every corner on a slider with three stops, the Lesser Golden Cut, the Archimedean cut and the Greater Golden Cut (on the octahedron DICTO's Unborn Axes and Icosaxes), opened directly by polyhedraverse.dictospheres.com/?open=goldencut:DODECAHEDRON (src/app/golden-cut-geometry.js, src/app/golden-cut-lens.js). The HexOct kit and Kaleidohedra's HexOct world (paper #75) pick their tile pair: #75's tiles or a pair of the HexOct family (paper #86, DICTO DOI 10.5281/zenodo.23896076), A · HexOct 3/8 to E · HexOct 1/10, every tile one solid (A: a brick of two cubes and the twisted cube), opened directly by kaleidohedra.dictospheres.com/?open=hexoct:3C:A and polyhedraverse.dictospheres.com/?open=hexoctkit:3C:A (src/app/hexoct-geometry.js, src/app/tile-surface.js).
It began with two shapes DICTO found by building with their hands: a golden leaning hexagonal prism, and a skewed rhombic dodecahedron that fills space as a sheared FCC lattice (first notes in Polyhedraverse's docs/). Everything since grew from asking what else such shapes can do.
This is the beginning of the README. Read the rest at the original. Read the full README ↗
