Zing Origami - Polyhedra
The shape is two intersecting cubes, and the color change makes each one of the cubes a different color. This means that the color changes need to alternate in a checker or zigzag pattern. The model begins with a 7-by-9 rectangle. It could be folded from a square, but then the first step is to fold two edges under.
Dimpled Dodecahedron
2014
The shape is a shape based on the regular dodecahedron, a platonic solid composed of twelve regular pentagons. The dimpled version replaces each face with a smaller, inverted pentagon, and each vertex with a sunken pyramid. This shape is equivalent to a semi-sunken variation of the Archimedean solid the Snub Dodecahedron. It is also interesting in the the convex edges describe six great circles.
The shape is a shape based on the regular dodecahedron, a platonic solid composed of twelve regular pentagons. The dimpled version replaces each face with a smaller, inverted pentagon, and each vertex with a sunken pyramid. This shape is equivalent to a semi-sunken variation of the Archimedean solid the Snub Dodecahedron. It is also interesting in the the convex edges describe six great circles.
Dual Cube
2011
The shape is two intersecting cubes. I first saw it in an M. C. Escher print many years ago. The model is folded from a single sheet of paper, a rectangle with a 2:1 ratio. Still, this is only a preliminary study. My goal is to fold it from a square and with a color change so that the two cubes are in contrasting colors. This will require six color change regions. Fortunately I have a method for this, similar to the way I affect the color change in my Stellated Octahedron.
The shape is two intersecting cubes. I first saw it in an M. C. Escher print many years ago. The model is folded from a single sheet of paper, a rectangle with a 2:1 ratio. Still, this is only a preliminary study. My goal is to fold it from a square and with a color change so that the two cubes are in contrasting colors. This will require six color change regions. Fortunately I have a method for this, similar to the way I affect the color change in my Stellated Octahedron.
Dual Color Stellated Octahedron
2010
Single-sheet stellated polyhedra are pretty advanced but the color change brings it to a whole 'nuther level of complexity. The first challenge was to work out how to achieve the arrangement of alternating colors. I needed two corners to come to the center like a blintz but offset. Working out the amount of offset for the grid to be the right size was the key problem. It turns out the angle is 67.5 degrees, which is 3/4 of 90 degrees and easily derived. It also has a slope of 3/2, which is also easily derived from a square grid. From this I was able to work out the arrangement of the squares in the inner rotated grid and the outer triangular grid areas, which correspond to the blintzed flaps. The 3/2 slope made was convenient because the grid is has an integer relation of the unit the whole. Each square of the grid has a length of 2/13 the edge of the paper, as you can see in the crease pattern.
Single-sheet stellated polyhedra are pretty advanced but the color change brings it to a whole 'nuther level of complexity. The first challenge was to work out how to achieve the arrangement of alternating colors. I needed two corners to come to the center like a blintz but offset. Working out the amount of offset for the grid to be the right size was the key problem. It turns out the angle is 67.5 degrees, which is 3/4 of 90 degrees and easily derived. It also has a slope of 3/2, which is also easily derived from a square grid. From this I was able to work out the arrangement of the squares in the inner rotated grid and the outer triangular grid areas, which correspond to the blintzed flaps. The 3/2 slope made was convenient because the grid is has an integer relation of the unit the whole. Each square of the grid has a length of 2/13 the edge of the paper, as you can see in the crease pattern.
Sphere
2008
An approximation of a sphere. I developed 32- and 72-facet versions. It's a nice layout but difficult to fold well. Fun fact: "Sphere" is Thelonious Monk's middle name.
Truncated Octahedron
2008
This fourteen-sided Archimedean solid has six regular hexagons and eight squares as faces. I designed this on a trip to Washington D. C. Folded from a single square sheet.
This fourteen-sided Archimedean solid has six regular hexagons and eight squares as faces. I designed this on a trip to Washington D. C. Folded from a single square sheet.
