What basic geometric shapes, besides cubes, interlock "minecraft" style like cubes?

A small edit to make question more suited to Game Dev:

I am experimenting with game dynamics to create geometric solids interlock seamlessly on their faces much the way the cubes do in minecraft. The objective is to create an interlock system that is also memory efficient consistent enough to maintain interlock over the course of many connections without deviating from the main grid.

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    \$\begingroup\$ You'd probably be interested in Tessellation and it might be worth asking one of the math stackexchanges. Any particular reason this might relate to a game where you'd want to rephrase your question to reflect that? \$\endgroup\$ – Coburn Aug 29 '16 at 1:54
  • \$\begingroup\$ mathforum.org/sanders/geometry/GP07Tessellations.html \$\endgroup\$ – Jaxkr Aug 29 '16 at 2:25
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    \$\begingroup\$ I agree that this question would be better suited to a math StackExchange. Just because you're using a piece of math within a game doesn't necessarily mean a game developer will give you a better answer about the math part than a mathematician would. ;) To get you started, the term you're looking for in 3D is Space-Filling Polyhedra. Swing back here if you need tips on implementing these structures, once you've settled on the grid system you want to use. \$\endgroup\$ – DMGregory Aug 29 '16 at 2:53
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    \$\begingroup\$ The one gamedev-specific bit of advice I can give is that these polyhedra become less intuitive for a player to manage & visualize very quickly once we move past cubes. So if the player has to interact directly with this interlocking system, you need to be very conscious of the complexity each alternative brings. If the choice to use a non-cube system is mainly for style, consider whether you can apply decorative effects to visually distinguish the results, without overcomplicating the underlying tiling grid. \$\endgroup\$ – DMGregory Aug 29 '16 at 3:01
  • \$\begingroup\$ That is actually a very good point thank you very much. Sometimes these ideas are innovative as inventing an elevator that moves sideways :D \$\endgroup\$ – Pipsqweek Aug 29 '16 at 3:59

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