Crystalline geometry; a projection from five dimensions into three.

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This sculptural, low-relief “slice” of crystalline geometry is a mathematical projection from five-dimensions into three.

When you move from one dimension to another circles become ellipses and angles change. My sculpture mimics a plane cast obliquely through a grid of hypercubes showing the conjoined surfaces. Fragments of the square faces of hypercubes have become skewed into diamond shapes. The sculpture is made from just one identical repeating shape, a rhombus with diagonals in the Golden Ratio.

The painted glass tiles are assembled according to certain mathematical matching rules that I’ve coded into a Baroque design, carved into rubber and printed on the glass. Each tile is printed and kiln-fired with traditional stained glass enamels, then painted several more times before being wrapped in adhesive copper tape. The tiles are then soldered together to build the sculpture. Below, copper-foiled glass tiles stacked in boxes and a small section tack-soldered together.

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The tiles fit together easily to form convex or concave rosettes with five ‘petals’. They also form groups of three, either shallow dishes or steeper ‘ears’. When the tiles are correctly conjoined my painted pattern flows through from tile to tile, creating a cohesive overall design. If each tile is also located correctly in three-dimensions the sculpture can grow infinitely without repeating itself, by simply adding more tiles.

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When light is cast through the sculpture onto a parallel surface the stained glass projects a two-dimensional image of another geometric pattern. Discovered in the late 1970’s and called  Penrose tiling, this pattern is made up from two different tiles. This also is beautiful and fascinating, and I have been obsessed with it since I was a post-grad student at the Royal College of Art in 1984.

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I had the lovely opportunity to meet Sir Roger last year for lunch at Yale and show him my model for this sculpture. I also took a stained glass panel I’d made some years before with his famous tiling pattern in it. This was the last of my Menfolk series and the beginning of my full-time focus on stained glass geometry.

I’ve received a lot of encouragement along the way, especially from computer scientist Duane Bailey who has been researching Penrose tiling for decades. When I met Duane almost four years ago we were both working in two-dimensions. This past July we started working together in three.

We have built three sculptural models so far, each with over 500 tiles the size and shape of business cards. We have designed four more sculptures. Each uses colour to explore some particular aspect of the geometry.

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The assembly was fiddly and time consuming, but well-worth the effort.

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The reverse of the sculpture is beautiful too. Each tile is made from a plain folded business card, and the triangular folded-back corners cluster together like the petals of mountain laurel.

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I learned such a lot about the this geometry. That it grows from seeds that change  shape depending upon where you begin. That it has kingdoms, worms and skeps, and more rules called inflation hierarchies to be taken into account. The surface can fold up to nest over itself in curious ways.

Remarkably, this pattern also models the structure of quasicrystals, materials that exhibit long-range order at a molecular level but lack any of the classic symmetries that characterize conventional crystals. Quasicrystals are neither amorphous solids (like glass or plastic) or regular crystalline materials (like salt or diamonds). They exhibit a host of unusual physical properties and can be made to self-assemble from nanoparticles to make invisible materials.

Making life-sized models of molecular structures in glass is pretty neat, and building something by hand (rather than modeling on a computer) provides wonderful insights. It may be difficult to visualize a skewed five-dimensional cube being ‘projected’ into another dimension) but the relationship between sculpture and cast image is really quite simple, and elegant to witness.

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Stained Glass Tiling: the process

Williams College student Elizabeth Jacobsen describes the process of designing and building a stained glass window from a mosaic of transparent colored glass tiles, each handpainted and kiln fired to create a unique work of art.

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2016 workshops

workshop(front)This year, I am offering week-long design and glasspainting workshops in June; 3-hour Saturday Afternoon Intensives; and a 10 week series of evening classes beginning March 10th. All at my studio in Vermont. Here’s the schedule. Application deadlines for American Glass Guild and Stained Glass Associate of America scholarships are Feb 28th and April 13th respectively.

 

The Mohawk prisms

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I have a lovely project underway at the moment: new 1930’s style signage for the Mohawk Bar in North Adams, Massachusetts, to tie in with their original windows made from ribbed glass tiles. Designed to bring more daylight into the interior of stores and factories, these pressed/cast tiles were widely produced and very fashionable in the days before electric lighting.

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I adapted the classic typeface Broadway, adding ‘etched’ lines (decorative parallels on the wide strokes) to provide positions for leadlines that wouldn’t interfere with reading the text.

Thanks to colleagues David Guarducci in Great Barrington, and to Scott, Fred and Sue Shea at Stained Glass Resources (sometimes it takes a village!) I managed to get ahold of some French Verierre de Saint Gobain ruby-on-white flashed glass. The ruby surface of this two-coloured sheet glass can be etched away to expose a clear or amber underlayer.

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Sandblasting was done by my good friend and neighbor, sculptor Bill LeQuier, who also carves ocean waves in glass.

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I used black masking tape on top of contact paper to mask out the areas to be sandblasted. Next, each pane is painted and fired. My proprietary glasspainting recipe is great for obtaining solid blacks first time over the ruby background.

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Careful measurement and old-fashioned geometry.

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The existing windows are simple grids of 4″ squares. Washed and polished, they sparkle like new.

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Using a portable band saw to cut the zinc profiles.

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I’m seriously enjoying working with a new material… cutting miters, filing to precise dimensions. The zinc behaves quite differently to lead. The first panel is now assembled, ready to be soldered, puttied, patinated and polished.

More about the Mohawk project and project developers Moresi & Associates

Reception, 12-1 on Thursday, for Stained Glass Tiling

My Winter Study students will be showing their stained glass tilings at Williams College on Thursday January 29th, from 12 – 1pm. Everyone is welcome. The exhibition will be held in the 3rd floor corridor (overlooking the atrium cafe) between the Chemistry and Physics buildings. Enter the cafe from the Science Quad and look for signs. The best place to park is at the far end of the public lot across from Tunnel City Coffee.

Ten students have created unique and personal works of art. Here’s a taster: details of stained glass windows designed, cut, hand-painted, kiln-fired and assembled by Julia Damion and Ivy Ciaburri.

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Three days in the belfry..

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Hurrah! I just installed three more windows for Trinity Episcopal in Branford, Connnecticut, to accompany the Archie Hanna Memorial window (2013) and complete the facade that looks out onto the village green.

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Above, the design; below, sections of the finished stained glass in the studio.

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The rose window was made in pieces to fit into an original wooden window frame with curved tracery. The 162-year-old woodwork is sound and sturdy but the window frame had bowed and distorted somewhat over the years; the individual openings for the glass were far from symmetrical! Richard fabricated a carefully measured steel yoke to hold the old wooden frame securely in place for another few hundred years or so.

I spent three days amongst the dust and pigeon poo in the belfry removing old glass; cleaning, restoring and painting the old wood frame; and installing my new window.

Access to the bell tower was via a cupboard door on the choir loft. From there, all of our tools, materials and the new stained glass window had to be hauled up on a rope. We made the 35ft ascent dozens of times over the three day installation, climbing like monkeys up a succession of 1″ thick wooden battens that had been nailed to the beams of the church. The access shaft was barely 2ft wide (fine for me, but a bit of a squeeze for Richard!).

I took the last photo with my iPhone, looking down over the toe of my shoe before descending through the darkness once again, groping to keep my footing. See our yellow rope fresh from hauling up a broom and some tubes of caulk, and the orange extension cord dangling into the abyss.

The two little arched windows, each about 4ft tall, had their own special challenges to keep us on our toes. One was in a very small cupboard, the other perched over a stairwell, requiring an asymmetric ladder.

Back in the summer we removed the old sashes and created new stops at the window sills. I made cardboard templates of the openings for building the two new windows. As with the rose, nothing was neat or symmetrical. The new stained glass was held in place with pre-cut curved wood trim, sealed against the weather with compressible foam tape. Each has an aluminum H-bar for support that we’d prepped beforehand in the studio.

Why make stained glass for a cupboard? Or for the bell tower where no-one will see it?

These last three windows are intended to be seen from outdoors, to complement and support the Hanna Memorial window. The stained glass will be illuminated from dusk ’til dawn, lighting up the facade of this lovely old New England church.

Hanna Memorial window. Stained glass by Debora Coombs for Trinity Episcopal, Branford CT showing the Holy Family by the Sea.

Last year I posted lots technical information about the Archie Hanna memorial window (above) including cartooning, colour selection, glass cutting, sandblasting, painting and fabrication. There are some real-time videos of glasspainting too. The window shows the Holy Family by the Sea, with Joseph holding baby Jesus beside a salt marsh with, apple blossom, roses, wheeling seagulls and more. Browse through these by clicking ‘ Trinity Branford’ in the word cloud underneath the Search box to the right.

 

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The last of the Roses 2

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There’s nothing more satisfying than cutting long beautiful miters out of 1/2″ wide lead…

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…and seeing the last few pieces of glass fit together on a project.

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The last of the roses for Trinity Episcopal in Branford Connecticut.

Hurrah!