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This origami tessellation is based off a pretty simple idea that I had. But since its design allows for so many shapes in a relatively small amount of space, it winds up looking v...
I recently showed you that if you take the regular icosahedron: considered in a coordinate system based on the golden ratio, and then replace в€љ5 by -в€љ5 in all your formulas, yo...
Six 1 × 1 rhombus are removed from the six corners of a regular 6 × 6 hexagon as shown. Each small triangle has unit area. What’s the area of the largest regular hexagon (not nece...
You are given 12 regular pentagons of the same size. You are also given 12 fixed points on the plane. Can you always place the pentagons such that no two overlap and all points are...
Here's a new flagstone tessellation using trapezoids in yet another way. They truly are the most versatile of all the standard shapes in origami tessellations. I used to think it w...
This is a difficult origami tessellation that uses collapsed hexagons to create series of 12 rhombuses around a center point instead of the typical set of six. The hexagon collaps...
This is a flagstone tessellation that utilizes alternating trapezoids and triangles spinning around a small hexagon on the other side. What this particular starting point creates...
This is a tessellation from back in mid May. It's kind of a weird one. It starts with a collapsed hexagon and then there are teardrop shapes tucked into it. In order to repeat the...
I was shown this puzzle in March 1997, the original source is unknown to me and I've tidied it up a bit to make it possible to solve without a calculator (calculators still allowed...
Here we have a level 2 Sierpiński carpet, obtained by taking a square, dividing it into 9 squares that are 1/3 of its size, removing the middle square, and repeating the process a...
I don't really remember this intermediate tessellation from a few weeks ago. Had to unfold it to determine the structure. Looking at the finished photo doesn't really reveal any c...
Every once in a while I'll come up with an unusual configuration of rhombus twists that I use to create a new tessellation. Unlike traditional twist based rhombus tessellations, t...
This is a pretty simple original origami tessellation that uses the natural twist of an open back hexagon to create multiples series of spinning miniature house shapes. The unique...
In the image: ABCDE is a regular pentagon F, A, B are colinear G, E, C are colinear FA has half the length of EC BCGF is a parallelogram Which area is bigger: the regular pentago...
What proportion of the outline pentagram is covered by the inner pentagrams? The illustration only shows 4 levels of iteration of pentagram, but consider if the series went to the...
link to full size image opens in google photos. This original origami tessellation is fully twist based, but gives the appearance of something more complicated. It actually uses a...
Uniformly random point P is chosen inside a regular heptagon with neighbouring vertices A and B. What is the expected number of vertices between ray AP and ray BP? Here is an examp...
This is an intermediate origami tessellation that I did last week. It's a simple design that creates an interesting pattern. Not every tessellation has to be intricate or complica...
This is a difficult tessellation that I recently conceived and folded. It's a hybrid design of tucks, collapses and twists. It's quite a dense pattern that is pretty labor intensi...
This is a twist based tessellation that I created a few weeks ago. I was just looking for an unusual pattern that could work without too much fuss. I had the idea to rotate 3 trap...
Here are two thick forward and backward slashes, each made of two isosceles right triangles glued along the smaller sides. For what values of n can you wrap n forward slashes and...
Here's kind of a cool flagstone tessellation that I created recently. It looks somewhat random, but it really isn't. The center point is six rhombuses around a small hexagon on th...
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