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Sliceform in paper. This form is the result of experiments in 3D Studio using tunnel shaped voids.

 

95x95x95mm

I'm pleased with how this one turned out - the colors and diamond shapes remind me of stained-glass mosaics!

This has been on my to-do list for a while. Doubled motifs are commonly found in traditional Islamic geometric artwork, so I'm happy I finally got to pay homage with a paper sliceform interpretation!

A festive sliceform for the holidays! Can you see the two overlapping pentagons that form the decagon?

Zillij by Chris K Palmer, (modified from a traditional design by his student Elizabeth Ager), 2009, 12" diameter. Cut on the Craft ROBO Pro and assembled by Jeffrey Rutzky.

 

Video version:

www.youtube.com/watch?v=2TNUxWVgZTs

 

While teaching architecture at the University of Colorado–Boulder, Chris K Palmer developed Rhinoscripts to calculate intersecting “ribs.” Using several variables, such as material thicknesses, the script automatically generates vector-based files that, in turn, are used to drive CNC machines (laser and Craft ROBO cutters, 3-axis routers). Not only has Palmer expressed his favorite traditional Middle Eastern patterns, but he also has built, with his students, life-sized domed structures. All models assemble without external fasteners or adhesives, and use only the flat parts themselves, much like sliceforms.

 

Creating forms using the box slot connection began with work by Akio Hizume, who wrote custom software to calculate patterns, as well as scale and life-sized towers.

I could spend hours staring at this dense packing of octagonal stars!

A square design composed of 16 and 8-sided rosettes. Hand for scale :)

Sliceform in paper.

 

95x95x95mm

Constructed using cardboard packaging. Maquette for rapid-prototype.

 

135x135x135mm

Sliceform in paper.

 

95x95x95mm

A sphere paper sliceform model. The circles are printed out then all slots are hand measured and cut. Each sheet is spaced 5mm apart.

Playing with 3-dimensionality. Besides, why make one sliceform when you can make four? :)

I could stare at this pattern for hours. If you look closely, the piece packs 4-sided, 5-sided, 6-sided, 7-sided and 8-sided stars beside each other! Yet we know from analyzing the angles that such a set of regular polygons could never tile the plane: en.wikipedia.org/…/Euclidean_tilings_by_convex_regu…

 

The answer is that some of the polygons are ever-so-slightly irregular to fit with each other, even though to the eye they all appear deceptively regular.

 

I first discovered this tiling in Craig Kaplan's 2005 "polygons-in-contact" paper; it also appears in Tilings and Patterns by Grunbaum and Shepard and the Bourgoin plates. Pass it on: more people should learn about this almost-regular tiling!

12-fold patterns never get old!

Here's a piece I worked out based on a similar motif in Abas and Salman! The 12-sided rosettes are stacked in a square grid.

 

My favorite part is how several line segments line up and seem to outline a square frame around each rosette, even though there is no one contiguous strip that forms the border!

Hi all, another sliceform as apology for being away for so long!! Pattern as usual derived using the wonderful utility taprats. This one is especially exciting because over this summer I learnt how to use a laser cutter. That's right -- each strip is laser-cut instead of manually hand-cut by me -- which cut down the production time for this from ~12 hours to a paltry 6. :P

 

I've since had some success figuring out how to automate the process further by fiddling with Python svg libraries. Hopefully you'll see more updates this fall :)

I've always really liked Girih (www.flickr.com/photos/limitedcake/4807111016/), because quasiperiodic patterns are super cool :). Five years on, I thought it would be nice to revisit this motif again with improved technique and more precise proportions.

 

The decagonal pattern is historical, and I worked out the dimensions with the help of Lu and Steinhardt's paper (www.sciencemag.org/content/315/5815/1106). The pentagonal star embellishment around the border is mine.

Same motif as Royalty (March, 2016), but stacked in a hexagonal grid instead of a square one.

Zillij 5 & 10 by Chris K Palmer, 2009, 10.5" diameter. Cut on the Craft ROBO Pro and assembled by Jeffrey Rutzky.

 

Video version:

www.youtube.com/watch?v=yEnbIm_9Ejw

 

While teaching architecture at the University of Colorado–Boulder, Chris K Palmer developed Rhinoscripts to calculate intersecting “ribs.” Using several variables, such as material thicknesses, the script automatically generates vector-based files that, in turn, are used to drive CNC machines (laser and Craft ROBO cutters, 3-axis routers). Not only has Palmer expressed his favorite traditional Middle Eastern patterns, but he also has built, with his students, life-sized domed structures. All models assemble without external fasteners or adhesives, and use only the flat parts themselves, much like sliceforms.

 

Creating forms using the box slot connection began with work by Akio Hizume, who wrote custom software to calculate patterns, as well as scale and life-sized towers.

collapsible (sliceform) model based on the new london landmark

Haven't updated in a while! Here's a neat little sliceform that evokes to me the richness of marine life and algal blooms.

 

My favorite thing about Islamic geometry is how different features reveal themselves to you at different magnifications. When you peer at it closely, you see the intricacies of the 12-sided rosettes. If you step back however, you see instead a Star of David traced in negative space!

Many of my designs are original, but this one is plucked right from the history books. Heptagons or 14-gons aren't very common in traditional Islamic designs because they don't tile well, but here's one possible way to fit pairs of heptagons in between 14-gons!

NUS Year Two Plywood Construction project 2007

Courtesy of Yeow Yeow

Playing around with pentagons...

Fun with nonagons and hexagons!

Created by Oschene.

Template.

Messmerizing object, Thanks !

 

This was a pattern in a goodie bag of exchange gifts for the G4G7 Gathering for Gardiner Conference held annually in Atlanta. I didn't go, but when I saw the pattern I said to myself, “This reminds me of Ramin Razani’s stuff, which I love...I must contact Hans to get a PDF to ROBO it.” I sure wasn't going to manually cut-n-score this puppy! In fact, what's preventing me from making much of Razani’s work is that I’d have to redraw it from scan-scratch to make it ROBO-ready.

 

This took 1-1/2 hours to fold, but less than five minutes to minimally prepare the file for ROBO and then cut-n-score both sides. No X-Acto or scoring tool was used! Not even tweezers; only fingers.

 

Hans has many incredible sculptures, lamps, sliceforms, and other math- and art-related ephemera on his web site Glass Geometry.

This is the smallest sliceform I've done yet! The secondary stars needed tweezers to shape, but I really like the result.

 

The design is based off #20 in Bourgoin's plates.

Zillij 5 & 10 by Chris K Palmer, 2009, 16"; diameter. Cut on the Craft ROBO Pro and assembled by Jeffrey Rutzky.

 

Video version:

www.youtube.com/watch?v=BdSgu5UYkyI

 

While teaching architecture at the University of Colorado–Boulder, Chris K Palmer developed Rhinoscripts to calculate intersecting “ribs.” Using several variables, such as material thicknesses, the script automatically generates vector-based files that, in turn, are used to drive CNC machines (laser and Craft ROBO cutters, 3-axis routers). Not only has Palmer expressed his favorite traditional Middle Eastern patterns, but he also has built, with his students, life-sized domed structures. All models assemble without external fasteners or adhesives, and use only the flat parts themselves, much like sliceforms.

 

Creating forms using the box slot connection began with work by Akio Hizume, who wrote custom software to calculate patterns, as well as scale and life-sized towers.

The crown piece of the collection. I really liked the way the shadows played out in this photograph.

Here's the first sliceform of 2016! :) The composition is a fairly straightforward combination of 9-fold and 12-fold rosettes, but I was really pleased with how the 3-fold color symmetry turned out!

 

P.S. I have a Facebook page now! www.facebook.com/sliceformstudio/

Here's another 3D sliceform I've been thinking about for a while. This is a different style than the past few pieces I've done in that every strip is an identical accordion with equidistant slits, so no pre-tracing or calculations are needed.

 

This is exactly like Melisande's basic zillij form, just that instead of zigzagging through a hexagonal grid, the underlying tiles are hexagons, pentagons and heptagons. This is very much like how many people have built origami tori with PHiZZ units!

 

Since every strip traces out a closed loop, there are no open ends here. You can see some imperfections (where I glued two ends together) if you look at the top rim of the closest cross-section :P.

The result of a late night of playing around to learn Solidworks. A fun example of the endless possibilities for design.

 

NOTE: I think the original size makes a lovely desktop background, though I admit my opinion is a bit biased.

New year, old model. Here's an updated and better photo of Constellation II, a paper strip sliceform I made in 2014 featuring 12-sided and 6-sided rosettes!

This particular concept has been on my mind for the longest time, but I've only recently acquired the tools to make it a reality. :)

 

More math in this one than usual -- each curve is a logarithmic spiral. I was going for the Fibonacci combination of 21 one way and 34 the other (enrichla.org/fibonacci-flowers/) but the parity didn't work out. This is 21 vs 33... close enough :P.

 

Arc lengths computed in Mathematica, SVG generated in Python and then cut with a laser cutter. Hand assembled.

 

Happy holidays everyone :)

This particular concept has been on my mind for the longest time, but I've only recently acquired the tools to make it a reality. :)

 

More math in this one than usual -- each curve is a logarithmic spiral. I was going for the Fibonacci combination of 21 one way and 34 the other (enrichla.org/fibonacci-flowers/) but the parity didn't work out. This is 21 vs 33... close enough :P.

 

Arc lengths computed in Mathematica, SVG generated in Python and then cut with a laser cutter. Hand assembled.

 

Happy holidays everyone :)

Another snow day, another assembly!

 

This piece incorporates traditional Islamic rosette motifs, but surrounds them with rings of diamonds -- I really like the effect. :)

 

This took ~9 hours to assemble; not the most time-consuming piece I've done, but one of the most intricate. The reason for this is because strips don't extend radially from the center, but weave in and out (see the orbit of the green strip in my schematic: www.dropbox.com/s/k50tpkdf9qkc9qu/orbit.png). My technique improved a lot in making this, though!

 

There are no closed loops in this piece, so it should be possible to assemble with just paper, no glue. That said, I had to use glue on 2-3 occasions because I made a couple mistakes. Can you spot any of them? :P

 

(Hint: the topmost rosette is a bit misshapen...)

Roughly 1800 individual pieces of plexi in a single, interconnected eggcrate construction, represents the upper 300 meters of an 870 meter tall tower.

 

Areas of development (red) occur sporadically as the market demands within a larger system of structure and infrastructure (white, spaced five floors apart) which occasionally houses large cultural attractions (pods)

Critic: Hani Rashid

I decided to return to the 3D sliceform arena with my newfound laser cutting skills! I'm pretty pleased with this as it ended up a lot more circular and stable than my previous 3D piece (www.flickr.com/photos/limitedcake/6230783292/)

 

This piece has the distinction of having no open ends -- each paper strip ends up as a closed loop. This proved pretty challenging for construction; I had to start radially from one "pole" and then glue the open ends together at the antipodal point (you can see one such seam on the black strip near the top of the photo).

 

The underlying shape is a truncated-truncated-icosahedron, with 12 decagonal rosettes and 20 dodecagonal rosettes.

I've been experimenting with various small motifs and learning about how well they translate to a good sliceform design. So far, this is one of my favorites – a 10-sided rosette surrounded by 10 pentagonal rosettes.

I've hit a few mental roadblocks with designing recently, where I start a motif and then abandon it because the symmetry or the proportions don't look great. To get over this I decided to spend some time going back to the "classics". Here's a fairly traditional motif from Eric Broug's book, Islamic Geometric Design.

 

I'm a big fan of the six-way symmetry inscribed within the 12-sided star. I could just stare at this for hours and admire how the lines and shapes flow into each other! Can you also see the equilateral triangles and the squares hiding in this? :)

Zillij 8 by Chris K Palmer, 2009, 15" diameter. Cut on the Craft ROBO Pro and assembled by Jeffrey Rutzky.

 

Video version:

www.youtube.com/watch?v=5MOLEzYcDNU

 

While teaching architecture at the University of Colorado–Boulder, Chris K Palmer developed Rhinoscripts to calculate intersecting “ribs.” Using several variables, such as material thicknesses, the script automatically generates vector-based files that, in turn, are used to drive CNC machines (laser and Craft ROBO cutters, 3-axis routers). Not only has Palmer expressed his favorite traditional Middle Eastern patterns, but he also has built, with his students, life-sized domed structures. All models assemble without external fasteners or adhesives, and use only the flat parts themselves, much like sliceforms.

 

Creating forms using the box slot connection began with work by Akio Hizume, who wrote custom software to calculate patterns, as well as scale and life-sized towers.

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