Close-Packing Spheres
Introduction - Simple Patterns

Play with these basic arrangements first. Try to understand what are the constrains and patterns imposed by space - START with these very simple combinations.
Explore the structures and understand the main fact - captured and exposed by each of these structures.
© 2016-2026 Platonic Structures Inc. All right reserved.

One Plane - Square Lattice

Square Lattice. Nodes: 225 Sticks: 420 Planes: 1 Time to build: 20 minutes.

One Plane - Hexagonal Lattice

Hexagonal Lattice. Nodes: 91 Sticks: 240 Planes: 1 Time to build: 15 min.

My 12 neighbours - Square Lattice

Square Lattice. Nodes: 13 Sticks: 36 Planes: 1 Time to build: 20 minutes.

My 12 neighbours - Hexagonal Lattice

Hexagonal Lattice. Nodes: 13 Sticks: 36 Planes: 3 Time to build: 15 minutes.

Three Planes - Square Lattice

Square Lattice. Nodes: 109 Sticks: 377 Planes: 3 Time to build: 35 minutes.

Three Planes - Hexagonal Lattice

Hexagonal Lattice. Nodes: 104 Sticks: 384 Planes: 3 Time to build: 25 minutes.

Central Sphere Pattern - Hexagonal Lattice

Hexagonal Lattice. Nodes: 84 Sticks: 336 Planes: 7 Time to build: 35 minutes.

Four Directions, 16 Lines - Hexagonal Lattice

Hexagonal Lattice. Nodes: 128 Sticks: 318 Planes: 7 Time to build: 35 minutes.

Classical Platonic Solids

Explore the five classical platonic structures: Tetrahedron, Octahedron, Cube, Icosahedron, and Dodecahedron. They are special because every face is a regular polygon of the same size and shape. Few varieties for each of these classical structures are included here.
© 2016-2026 Platonic Structures Inc. All right reserved.

Tetrahedron - Packed

Hexagonal Lattice. Nodes: 680 Sticks: 3360 Planes: 15 Time to build: 3.5 hours.

Octohedron - Thin Walls

Square Lattice. Nodes: 578 Sticks: 1728 Planes: 25 Time to build: 3.5 hours.

Cube - Packed

Square Lattice. Nodes: 4631 Sticks: 25200 Planes: 21 Time to build: 9.5 hours.

Icosahedron F5 - Frame

Square Lattice. Nodes: 3658 Sticks: 12236 Planes: 41 Time to build: 17 hours.

Icosahedron F7 - Frame

Square Lattice. Nodes: 6226 Sticks: 20380 Planes: 51 Time to build: 19 hours.

Dodecahedron Frame

Square Lattice. Nodes: 2482 Sticks: 7028 Planes: 37 Time to build: 15 hours.

Tetrahedron - Thick Walls

Hexagonal Lattice. Nodes: 596 Sticks: 2688 Planes: 15 Time to build: 3.5 hours.

Tetrahedron - Thin Walls

Hexagonal Lattice. Nodes: 394 Sticks: 1248 Planes: 15 Time to build: 3.5 hours.

Tetrahedron - Thin Walls With Holes

Hexagonal Lattice. Nodes: 310 Sticks: 924 Planes: 15 Time to build: 3.5 hours.

Tetrahedron - Thick Walls With Holes

Hexagonal Lattice. Nodes: 272 Sticks: 924 Planes: 15 Time to build: 3.5 hours.

Tetrahedron - Frames

Hexagonal Lattice. Nodes: 82 Sticks: 96 Planes: 15 Time to build: 30 minutes.

Octohedron - Packed

Square Lattice. Nodes: 1469 Sticks: 7800 Planes: 25 Time to build: 3.5 hours.

Octohedron - Thick Walls

Square Lattice. Nodes: 980 Sticks: 4380 Planes: 25 Time to build: 3.5 hours.

Octohedron - Thin Walls With Holes

Square Lattice. Nodes: 354 Sticks: 888 Planes: 25 Time to build: 3.5 hours.

Octohedron - Thick Walls With Holes

Square Lattice. Nodes: 468 Sticks: 1620 Planes: 25 Time to build: 3.5 hours.

Octohedron - Frames

Square Lattice. Nodes: 138 Sticks: 168 Planes: 25 Time to build: 30 minutes.

Cube - Thick Walls

Square Lattice. Nodes: 2174 Sticks: 8772 Planes: 21 Time to build: 3.5 hours.

Cube - Thin Walls

Square Lattice. Nodes: 1202 Sticks: 2520 Planes: 21 Time to build: 3.5 hours.

Cube - Thin Walls With Holes

Square Lattice. Nodes: 524 Sticks: 984 Planes: 16 Time to build: 3.5 hours.

Cube - Thick Walls With Holes

Square Lattice. Nodes: 916 Sticks: 3336 Planes: 16 Time to build: 3.5 hours.

Cube - Frames

Square Lattice. Nodes: 332 Sticks: 576 Planes: 16 Time to build: 1.5 hours.

Icosahedron F1 - Full

Square Lattice. Nodes: 892 Sticks: 4608 Planes: 15 Time to build: 4 hours.

Icosahedron F3 - Full

Square Lattice. Nodes: 5282 Sticks: 29220 Planes: 27 Time to build: 12 hours.

Icosahedron F1 - Frame

Square Lattice. Nodes: 486 Sticks: 1704 Planes: 15 Time to build: 15 hours.

Icosahedron F3 - Frame

Square Lattice. Nodes: 1822 Sticks: 6528 Planes: 27 Time to build: 19 hours.

Dodecahedron Full

Square Lattice. Nodes: 10122 Sticks: 56424 Planes: 37 Time to build: 19 hours.

Rhombic Dodecahedrons

Explore the Rhombic Dodecahedron - a convex polyhedron with 12 congruent rhombic faces. It has 24 edges, and 14 vertices of two types. It is a Catalan solid, and the dual polyhedron of the cuboctahedron.
© 2016-2026 Platonic Structures Inc. All right reserved.

Rhombic Dodecahedron - F4 - Packed

Square Lattice. Nodes: 93 Sticks: 384 Planes: 9 Time to build: 1.5 hours.

Rhombic Dodecahedron - F8 - Packed

Square Lattice. Nodes: 617 Sticks: 3072 Planes: 17 Time to build: 17 hours.

Rhombic Dodecahedron - F12 - Packed

Square Lattice. Nodes: 1957 Sticks: 10368 Planes: 25 Time to build: 3.5 hours.

Rhombic Dodecahedron - F16 - Packed

Square Lattice. Nodes: 1914 Sticks: 7404 Planes: 33 Time to build: 5.5 hours.

Rhombic Dodecahedron - F16 - Framed

Square Lattice. Nodes: 446 Sticks: 888 Planes: 33 Time to build: 4.5 hours.

Rhombic Dodecahedron - F20 - Thick Walls

Square Lattice. Nodes: 3035 Sticks: 11683 Planes: 41 Time to build: 13.5 hours.

Rhombic Dodecahedron - F20 - Thin Walls

Square Lattice. Nodes: 2284 Sticks: 6951 Planes: 41 Time to build: 8.5 hours.

Rhombic Dodecahedron - F20 - Thin Walls - With Holes

Square Lattice. Nodes: 1236 Sticks: 3326 Planes: 41 Time to build: 8.5 hours.

Rhombic Dodecahedron - F20 - Frames

Square Lattice. Nodes: 574 Sticks: 1136 Planes: 41 Time to build: 5.5 hours.

Rhombic Dodecahedron - One Plane

Square Lattice. Nodes: 502 Sticks: 2069 Planes: 1 Time to build: 1.5 hours.

Plane Tessellation

Explore the Plane Tessellation - the tiling of a plane, or a plane like surface, using one or more regular geometric shapes, called tiles, with no overlaps and no gaps. A periodic tiling has a repeating pattern. There are only eleven such arrangements possible.
© 2016-2026 Platonic Structures Inc. All right reserved.

Squares

Square Lattice. Nodes: 936 Sticks: 1056 Planes: 1 Time to build: 20 minutes.

Triangles

Hexagonal Lattice. Nodes: 461 Sticks: 660 Planes: 1 Time to build: 20 minutes.

Hexagons

Hexagonal Lattice. Nodes: 228 Sticks: 264 Planes: 1 Time to build: 20 minutes.

Hexagons-Triangles

Hexagonal Lattice. Nodes: 224 Struts: 296 Planes: 1 Time to build: 20 minutes,

Hexagons-Triangles-Triangles

Hexagonal Lattice. Nodes: 545 Sticks: 850 Planes: 1 Time to build: 20 minutes.

Squares-Triangles

Square Lattice. Nodes: 3085 Sticks: 8324 Planes: 25 Time to build: 2.5 hours.

Squares-Triangles-Triangles

Square Lattice. Nodes: 626 Sticks: 792 Planes: 7 Time to build: 2.5 hours.

Archimedean Solids

Comming Soon!
These Structures are built from identical nodes connected with each other using identical struts (links). Two patterns are available for you to use: square or hexagonal.
We are working hard to add more structures on this website for you to build. Check back soon for further updates.
© 2016-2026 Platonic Structures Inc. All right reserved.

Cuboctahedron - F2

Hexagonal Lattice. Nodes: 55 Sticks: 216 Planes: 5 Time to build: 1 hours.

Cuboctahedron - F3

Hexagonal Lattice. Nodes: 147 Sticks: 660 Planes: 7 Time to build: 1.2 hours.

Cuboctahedron - F4

Hexagonal Lattice. Nodes: 309 Sticks: 1488 Planes: 9 Time to build: 1.8 hours.

Cuboctahedron - F5

Hexagonal Lattice. Nodes: 561 Sticks: 2820 Planes: 11 Time to build: 2.2 hours.

Cuboctahedron - F5 - Thin Walls

Hexagonal Lattice. Nodes: 252 Sticks: 600 Planes: 11 Time to build: 2 hours.

Cuboctahedron - F5 - Thin Walls with Holes

Hexagonal Lattice. Nodes: 108 Sticks: 144 Planes: 11 Time to build: 2 hours.

Cuboctahedron - F6

Hexagonal Lattice. Nodes: 923 Sticks: 4776 Planes: 13 Time to build: 2.8 hours.

Cuboctahedron Variety 1 - F6

Hexagonal Lattice. Nodes: 642 Sticks: 2892 Planes: 13 Time to build: 2.8 hours.

Cuboctahedron - F7

Hexagonal Lattice. Nodes: 1415 Sticks: 7476 Planes: 15 Time to build: 3.8 hours.

Cuboctahedron - F7 - Thick Walls

Hexagonal Lattice. Nodes: 854 Sticks: 3564 Planes: 15 Time to build: 2.8 hours.

Cuboctahedron - F7 - Thick Walls with Holes

Hexagonal Lattice. Nodes: 636 Sticks: 2364 Planes: 15 Time to build: 2.5 hours.

Cuboctahedron - F7 - Thin Walls with Holes

Hexagonal Lattice. Nodes: 372 Sticks: 816 Planes: 15 Time to build: 1.5 hours.

Cuboctahedron - F7 - Frame

Hexagonal Lattice. Nodes: 156 Sticks: 192 Planes: 15 Time to build: 1.2 hours.

Truncated Octahedron - F1

Square Lattice. Nodes: 38 Sticks: 144 Planes: 5 Time to build: 20 minutes.

Truncated Octahedron - F2

Square Lattice. Nodes: 201 Sticks: 948 Planes: 9 Time to build: 35 minutes.

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