Hyper4D
English · Română · Français · Italiano · Español · Português · Deutsch · Magyar
Version: 2.2.0 (previous: v2.1.0) · Last updated: 2026-10-27
Status: stable · Offline: complete (no network needed)
Interface languages: Română, English, Français, Italiano, Español, Português (PT), Deutsch, Magyar
An interactive explorer of geometry in the fourth dimension: cross-sections of hyperbodies and projections of regular polytopes.
Live app: https://chiuta.github.io/Hyper4D/
What it is
Hyper4D is a single-file application (index.html, SVG + JavaScript, no libraries) for descriptive geometry "beyond the third dimension", in the style of a blue technical drawing. It has two categories: Cross-sections (what a 4D body looks like when cut by a 3D space, moving along the fourth axis) and Polytopes (4D → 3D → 2D projections rotated in real time).
Features
- Cross-sections: hypersphere, hypercone, hypercylinder, double hypercone (bicone), "STRING Pyramid", hypercylinder (construction), hyperellipsoid, oblique tesseract, unfolding (net). The r(w) profile with a point dragged by the mouse, the whole body with the current section, the "second cut" (sphere ∩ 2D = circle).
- For the hypersphere, views: section, "2 glued balls", "2 solid tori", "2 worms (the apple)" with a selectable number of worms.
- For the oblique tesseract: cutting directions face / edge / vertex.
- Polytopes: 5-cell, 8-cell, 16-cell, 24-cell, 600-cell, 120-cell; duoprisms (3,3), (3,5) and custom (P,Q); pyramids over the cube, octahedron, dodecahedron, icosahedron; "star skeleton".
- Double 4D rotation (the XW and YZ planes), perspective or orthographic projection, pause/play, speed, "Solid faces".
- More polytopes and 4D drag (v2.1.0): six new shapes under Polytopes — hyperprisms (polyhedron × segment) over the tetrahedron, octahedron, dodecahedron and icosahedron (8·16·14, 12·30·28, 40·80·54, 24·72·70 vertices·edges·faces), and the rectified 5-cell (10·30·30) and rectified tesseract (32·96·88; 64 triangles + 24 squares). All have uniform edge lengths and a passing Euler check (V − E + F − C = 0, with the cell counts 6, 10, 14, 22, 10, 24); the info texts exist in Romanian and English (other languages show English). New button “Drag rotates in 4D”: dragging then changes the XW (horizontal) and YZ (vertical) rotation angles instead of the 3D camera; holding Shift does the same for one drag; with the tutorial open it moves its XW/YZ sliders. The introductory tutorial for non-mathematicians already existed since v2.0.0 (below). Dragging has no keyboard equivalent; the tutorial sliders do.
- Interactive 4D tutorial (v2.0.0): dimensional analogy with a counting table (point to tesseract), six sliders for the XY, XZ, YZ, XW, YW, ZW rotation planes, automatic single-plane or double XW + YZ rotation, and switching between the tesseract, 24-cell and 120-cell. Texts in 8 languages; didactic values.
- Exact hypervolume and keyboard 4D rotation (v2.2.0): the title block now shows the exact V₄ (circumradius 1) for the hyperprisms, the rectified 5-cell/tesseract, the hyperpyramids and the duoprisms (including the custom P×Q one), each checked in the tests against an independent exact 4D convex-hull volume. 4D rotation from the keyboard: Shift + ←/→ rotates in the XW plane, Shift + ↑/↓ in the YZ plane (also drives the tutorial sliders).
- A title block with computed values (body, vertices·edges·faces — labelled V·M·F, S·A·F, V·E·F etc. depending on the language —, hypervolume V₄, the angles ∠XW and ∠YZ).
- Euler check for polytopes:
vertices − edges + faces − cells = 0, with vertices and edges counted from the drawn geometry (including for the custom P×Q duoprism); for duoprisms the polygonal faces of the bases are counted too, not only the square ones from the title block. It is not shown for the star skeleton.
New features (1.1.0)
Under Polytopes, below the diagram, a new row of buttons (in the app's 7 languages):
- OBJ export (3D): the polytope's vertices in the 4D → 3D projection at the moment of pressing (the current double rotation and perspective/orthographic mode) and the edges as
l lines. It opens in Blender, MeshLab etc. (pause the rotation so you know exactly what you are exporting). It does not export faces: it is only the lines (a skeleton).
- JSON export (4D): the 4D coordinates (x, y, z, w), normalised to circumradius 1, the edges and faces as indices (from 0), plus the counts. Tested: 8-cell = 16/32/24, 600-cell = 120/720, 120-cell = 600/1200 etc.
- QR code: the code contains the app's public address (
https://chiuta.github.io/Hyper4D/; when the page is served from another HTTPS host, the address of that page) plus the current state hash (language, category, shape, view). Useful for opening exactly the same view on a phone. The address can also be copied. Generated locally; it appears only if the QR module is in the file.
- Printing: the "Print" button (or Ctrl+P) now uses a stylesheet for paper: white background, dark lines, no tabs, buttons or selectors. Previously the dark theme was printed. The drawings remain those from the screen (the exact look of solid faces may differ from the browser's, depending on the printer).
The app's languages are EN, RO, FR, IT, ES, PT, DE, HU. The new translations in FR/IT/ES/PT/DE/HU are automatic, not natively checked.
The "fff-kit"
Modules pasted into index.html: core, label, bundle, qr. "Transparency" opens from the version in the footer (network: 0 external requests; there are no keys in localStorage, so the backup is empty). Without the kit, the app works the same, but without the QR button.
Tests
node tests/fff-r8.test.mjs (Playwright, network blocked; 41 checks): the OBJ export is compared independently with the 4D rotation computed from the JSON data and from the angles in the title block (orthographic and perspective), counts for 5-cell…120-cell and duoprisms, the tesseract's edge length, QR decoded back, labels in 8 languages, print mode (PDF), axe-core 0 violations (including the dialog, both categories), 360 px, without the kit.
User guide
- Choose the language from the selector in the corner of the header (EN / RO / FR / IT / ES / PT / DE / HU).
- Choose the category: Cross-sections or Polytopes.
- For sections: choose a body (for example "Hypersphere") and drag the point on the r(w) profile or move the
w slider to travel along the fourth axis; drag the body to rotate it.
- Tick "Show the cut toward 2D" (in the chosen language) for the second cut; for the hypersphere try the views "2 glued balls", "2 solid tori", "2 worms".
- For polytopes: choose a 4D polyhedron, then "Pause"/"Play" for the rotation, the speed slider and "Solid faces" for solid faces; switch between perspective and orthographic projection.
- For the custom duoprism choose the P and Q values from the lists.
- Copy the address from the browser to share exactly the current state (hash
#lang=…&cat=…&shape=…).
Privacy and network
- I found in the code no local storage (not even in 1.1.0: the exports are files downloaded on request) (
localStorage, IndexedDB), cookies or network calls (fetch/XHR); no external scripts, fonts or images are loaded.
- The navigation state is kept only in the URL hash (
replaceState).
- The only
http address in the file is the standard SVG namespace (www.w3.org), with no connection.
Running locally / offline
Download index.html and open it in a browser; it works fully without internet (the app's footer says: "Offline tool, no external dependencies").
History / Changelog
1.2.7 — 2026-10-23
- fff-kit 1.2.0 audit: the i18n-parity warning is a false positive (the keys are completed at run time); documented as a justified exception in
fff.config.json. No functional change.
1.2.5 — 2026-10-22
fff-kit 1.1.4: touch targets and minimum text size. Touch targets/text fixed in the app.
1.2.4 — 2026-10-22
fff-kit 1.1.2: PBKDF2 with 600,000 iterations, anti-clickjacking protection.
1.2.3 — 2026-10-22
- Mobile: text is at least 12 px and buttons and fields have larger touch targets on narrow screens.
- The “Buy Me a Coffee” button no longer floats over the controls; it sits at the end of the page.
1.2.2 — 2026-10-22
- Translation fix: the description (and name) in the transparency panel now follow the interface language.
1.2.1 — 2026-10-22
- The label of the glued-balls zone (poles, equator, toward A/B) is now translated and updates when the language changes.
14 October 2026 (v1.1.0)
- New under Polytopes: OBJ and JSON export, QR code of the state, print stylesheet; the "Transparency" window (fff-kit: core, label, bundle, qr);
tests/fff-r8.test.mjs. CSP: script hash recalculated.
12 October 2026 (v1.0.0)
- 1.0.0 — 2026-10-12: the version and the date of the last update are shown in the app
11 October 2026 (third entry)
- SVG saving for the polytope diagram and for the whole body + section.
- The rotating projection diagram is no longer
aria-hidden: it has a text description (body, V·M·F), updated when the shape or the language changes.
11 October 2026 (second entry)
- Euler check (V − E + F − C = 0) for convex polytopes, keyboard shortcuts
P/Space and ←/→, the title-block label V·M·F translated into all 7 languages (in English "M" made no sense), new translations in 7 languages.
- CSP policy:
script-src with a hash instead of 'unsafe-inline'.
11 October 2026
- Accessibility: the work area is wrapped in , the category bar became a
div element with the tablist role (axe: 0 violations).
- Added a strict CSP (no network, no external resources).
License
MIT for the app's code and structure — see the LICENSE file. Any third-party libraries included in the file keep their own licenses.
Author
Alexio — Alexandru-Ionuț Chiuță, contact: [email protected].
