Rhombs shaded on three faces so the surface reads as a stack of cubes seen from above

Isometric cubes

Three rhombs meet at every vertex of a hexagonal lattice. Shade them as a top, a left and a right face and the flat surface lifts into a stack of cubes. Nothing is drawn in perspective: the volume is entirely in the three tones.

Example

<?php

declare(strict_types=1);

use Atelier\Pattern\Pattern;
use Atelier\Pattern\PatternRegistry;
use Atelier\Svg\Document;
use Atelier\Svg\Dumper\CompactXmlDumper;
use Atelier\Svg\Element\Shape\RectElement;

require __DIR__.'/vendor/autoload.php';

$cubes = Pattern::isometricCubes(size: 22);

$document = Document::create(360, 200);

(new PatternRegistry($cubes))->attachTo($document);

$surface = new RectElement();
$surface->setX('0')->setY('0')->setWidth('360')->setHeight('200');
$surface->setAttribute('fill', $cubes->fill());

$document->getRootElement()?->appendChild($surface);

echo (new CompactXmlDumper())->dump($document);

Options

Setting	Default	Effect
`size`	`22`	edge of one rhomb, so the apparent size of a cube
`topFace`	`0.3`	opacity of the upper face
`leftFace`	`0.85`	opacity of the left face
`rightFace`	`0.55`	opacity of the right face
`withColor(string)`	`currentColor`	the single hue the three faces share
`withOpacity(?float)`	none	opacity of the whole tile, multiplied into the three faces
`withAngle(float)`	`0`	turns the whole paving through `patternTransform`
`withId(string)`	derived	fixes the identifier instead of deriving it from the tile content

Each face opacity must lie between 0 and 1, and throws InvalidArgumentException otherwise.

One hue, three opacities. The volume survives a change of colour and a change of theme, because it is carried by the contrast between the faces and not by the colours themselves. Move the three values closer together and the cubes flatten back into a lattice of rhombs.

How the tile closes

The rhombs form the rhombille tiling, the dual of the trihexagonal lattice: every hexagon of a honeycomb split into three rhombs meeting at its centre. Its smallest repeat is the same rectangle a honeycomb of the same size uses, one hexagon wide and two rows tall.

Rhombs cross the edges wherever a hexagon straddles them, so the tile draws the five lattice positions a honeycomb draws: the one that fits, and the four sitting on the edges, each present on both sides. A rhomb cut by the right edge finds its other half against the left edge, with the same face shading, so the cube it belongs to never changes tone across a seam.