Unit cell topologies reference

Grid

3 bars between opposing surface centers, crossing at the volume center.

When shifted by u/2 in XYZ this is also known as Cube.

X

4 space-diagonal bars crossing at the volume center (body-centered cubic without edges; also known as Cross)

Star

Like X but with 2 additional bars each from the volume center to top and bottom surface centers

W

Like X but with the corner points displaced towards -Y, -Z by 3u/10

E

Like Grid but with the 2 vertical bars omitted and instead with 4 additional bars, one each from the volume center along the XZ plane to the edge centers. Offset, this forms structures resembling "stacks of foldable camping chairs".

Column

1 single bar between the top and bottom surface centers

Trabecular

A random, biomimetic bar net focusing on average pore size rather than consistently sized, regular cell topology. Legacy use only.

Dark horse

9 bars in an arrangement remotely resembling a sawhorse, with a space-diagonal "spine" between two vertically asymmetric X shapes, one of them inverted. The pattern is repeated vertically in alternating checkers, rotated 90° around Z and space-diagonally shifted by u/2 in XY. This results in elongated lenticular pores, spanning 2u vertically and SQRT(2)u XY-diagonally, staggered and octahedrally packed in layers.

Penta cube

A pore of a near-regular dodecahedron, connected to others through mirror pairs of pores formed by truncated hexagonal trapezohedra, forming the Weaire-Phelan space-filling honeycomb

Soft box

Like Grid, but rotated, squashed, and tilted

Hexa grid

1u horizontal layers of oblong honeycombs along XY (2u X corner-to-corner, 1.5u Y edge-to-edge), with vertical connections between vertices

Hexagon

Pore of pole-truncated regular bipyramid (with its long horizontal edges omitted) at u/2 height, packed XY-diagonally and at a u/4 Z offset between packing layers.

Projection of such lattice in X or Y forms packed oblong hexagons (2u/3 XY corner-to-corner by u/2 Z edge-to-edge); projection in Z forms a truncated square tiling of 2u/3 octagons and u/3 squares.

Vin tiles

Fragments to form ideal Kelvin foam of tetragon-base, truncated octahedra.

To generate a complete pore within a single unit cell use an offset of u/2 in XYZ.

Cross pattee

24 bars forming three four-point stars, one along a cardinal plane each, crossing at the cell center. When shifted by u/2 in XYZ, bars form cross pattees along unit cell faces (Edge bars omitted).

Voronoi

Highly irregular, random, biomimetic bar web. Legacy use only.

Skeleton

Another highly irregular, random bar web. Legacy use only.

Octagon

Saddle-shaped 6-point star with tip-extending bars to connect space-diagonally through 6 of 8 cell corners. The connection along the space-diagonal between {-X, -Y, +Z} and {+X, +Y, -Z} is omitted.

Hexa profile

Like Hexagon but with angles adjusted to form exactly regular hexagons in cross section.

Snow flake

Like Octagon but "completed" for all eight corners. A cube with exaggerated tetrahedral points and tip-extending bars.

3D spider

8 S-curves between space-diagonally opposed cell corners, crossing through the cell center

Icosahedron

Pore of regular icosahedron oriented so that neighboring cells are touched by its edges. Edge bars also omitted.

Pyritohedron

Pore of regular dodecahedron oriented so that neighboring cells are touched by its edges

Rhombic dodecahedron

Pore of rhombic dodecahedron, perfectly packed with neighboring and offset-stacking pores of same geometry

Crush

Columns of zig-zagging bars, cross-linked at different points and in different directions

Tetra

Pores of 1u octahedra in face-centered cubic packing with pores of matching tetrahedra. Also known as octet-truss.