TOGridPile is a system of stackable cups based on a 1½″ unit cube, designed to be rotationally symmetric in 3 dimensions and allow subdivision down to ½″. There are several variations on the shape that are compatible with each other to varying degrees. Most are compatible with the 'beveled facerounded cube with columns' design described here.
It is similar to Gridfinity, but with a different unit size and edge profile.
It's kinda-sorta compatible with LEGO bricks, if you stack enough together. 5 TOGridPile atoms (2½″ = 63.5) ≈ 8 LEGO block widths (64mm), and 1 TOGridPile chunk (1½″ = 38.1mm) ≈ the height of 4 LEGO bricks stacked (38.4mm). There may have been a time before LEGO rounded their sizes to the nearest 1⁄10mm when these would have matched up exactly (source). This goes for Duplo and Mega Bloks also. Mega Bloks are 1¼″ wide and 1½″ tall, according to my calpiers.
The basic, symmetrical chunk shape is approximately a 1½″ cube (the 'chunk body') with ⅛″ beveled corners, plus a straight-sided column or foot that sticks out on each side.
More precisely, the chunk body is the convex hull of the six sides, each of which is a 1¼″ square (i.e. inset ⅛″ on each side) with 1⁄16″-radius rounded corners.
The cross section of the straight-sided columns are 1⁄16″-radius rounded, ⅛″-beveled, 1⅛″ squares. i.e. a square inset by 1⁄16″ on each side from the unit cube, with each edge shortened by ⅛″×2=¼″, and each corner rounded with a radius of 1⁄16″.
Chunks may be subdivided into ½″ atoms, with the same basic shape. A chunk is then made of 27 atoms, with the option to, for the body and/or the columns, take the convex hull of the corresponding part of the constituent atoms, or not.
In practice, most TOGridPile cups are only 'chunky' (or 'atomey') on the bottom, such that they can sit in a TOGridPile base plate (or across the tops of other TOGridPile blocks), but would not fit if turned sideways. Otherwise they would be very chunky indeed, and it would be impossible to have blocks with a lip on top, since the subtraction to hold the block above would completely obliterate the edges of the block below!
TOGridPile can be defined in terms of u (the lowest common denominator length unit, conventionally 1⁄16″, similar to that of LEGO bricks!), atom pitch (8 u = ½″), and chunk pitch (3 atoms = 1½″), and so variations can be easily derived simply by changing those numbers.
TGx9.4.scad is an OpenSCAD design for basic cups, with configurable size units, block size, bottom/lip segmentation, cavity size/subdivisions, and magnet/screw holes.