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Every hole you see belongs to one of two separate mazes. The gyroid is one continuous curved wall that winds through the whole ball and divides it into two channel systems that interlock everywhere but never meet. It contains no straight…
From the side it is a little Christmas tree; up close it is the same tetrahedron again and again. A Sierpinski tetrahedron is a tetrahedron made of four half-size tetrahedra, one at each corner, with the middle left empty. Each of those…
The oloid is the convex hull of two equal circles set at right angles, each passing through the other's centre. Give it a push and it wobbles along a meandering path, touching the table with every point of its curved surface as it rolls.…
Hold it up to a light and you can see straight through it, in three directions. A Menger sponge starts as a cube. Cut it into 27 smaller cubes, then take away the one in the middle and the six in the middles of the faces. Do the same to…
Take a double cone with a right-angled tip, cut it in half through its axis, and turn one half by 90 degrees. The result is the sphericon: it rolls in a zigzag, snaking path, and every point of its curved surface touches the table along…
Each cell of this ball is a hollow joint: six round tunnels meet in the middle, pointing up, down, left, right, forward and back. The cells join into one continuous wall. That wall splits the ball into two separate tunnel networks, which…
Draw an equilateral triangle, then replace each side with an arc centred on the opposite corner. The result is a Reuleaux triangle: a curve of constant width. Measure it with calipers at any angle and you get the same number; roll it…
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