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My initial studies stemmed from researching into Stellation. This, in simple terms, is the process of extending  polygon in two dimensions, polyhedron in three dimensions, or, in general, a polytope in n dimensions, to form a new figure. Through researching the application of this process, I came across the sculptures created by George Hart, as he has experimented with stellated geometries to which are subdivided to create mathematical interweaving structures.Stellation 1

My Research into the method and calculations of George Hart’s Mathematical Sculpture’s focused on the sculpture ‘Frabjous’. Through rigorous testing and model making I have understood the rules behind the complex form. This is based on the form of a stellated icosahedron, whose shape is contained within a dodecahedron.grey card model

Lines are drawn from one point, to a point mirrored at one edge of the face of the dodecahedron form – as shown in the diagram. This creates intersecting lines at each face as you can see from the diagrams below. Each dividing line has two intersection points, with symmetry at the center of the line. The sculpture aims to avoid the intersections of these lines by introducing a sine curve with the domain 0 to 2*pi. As you can see, each component is exactly the same – for this model, 30 components are used.

george hart diagram 1george hart diagram 2george hart diagram 3

`To simplify the construction of the sculpture, I extracted a build-able section which uses ten components in total. Two of these sections are then weaved together and joined up by a further ten single components to form the entire sculpture.Diagram Sequence of Researched SculptureOne Component ImageryGeometry 2

Following this research, I extracted the concept of avoiding the intersection and subdivided a cube with lines from each corner of the cube. These lines were then weaved around eachother using a sine curve with a domain of 0 to pi. I then mirrored the curves and rotated them to create an intertwining form.Avoiding Self Intersection 2

Another test was created with the same process, however subdividing a cube using the midpoint of each face. – This creates an octahedral geometry.Avoiding Self Intersection octahedron

Using this interweaving geometry, I have created different three dimensional arrays to create a spatial form. The concept of avoiding intersections naturally cause a structure to fail. To form a structurally efficient version of this geometry, I introduced the idea of a reciprocal structure, and allowed the beams to self support by resting on eachother. This did not create a structure strong enough to stand on, however through adding a cube whose dimensions are equal to the width of the beams, the structure became very strong.

Avoiding Self Intersection octahedron 3

Testing the component at a small scale required the design of a joint which allowed me to assemble these components together through interlocking elements. Each beam element slots into the joint; When two joints and two beams are connected together the curves naturally stay in place due to the angle cut into the joint. Three of these connected elements together form the component.

Diagraming the Joint

As mentioned previously, avoiding intersections create inefficient structures – For this small scale experimentation, the concept of Tensegrity was implemented. Tensegrity is a structural principle based on using isolated compression components within a net of continuous tension, allowing the compression members to not need to touch each other. This model was constructed using 1.5mm plywood which has been laser cut; the modularity of the system ensures minimal material wastage.

Construction Sequence of ModelModel Photographs

The three dimensional array of this geometry creates many interesting shapes and patterns when viewed from different angles – this is visible in the following video:

 

 

 

 

The history of curved crease folding goes back to as early as the Bauhaus, where a student had scored circular creases onto a paper in order to study its materiality. When a circular surface is folded along concentric rings, the resultant form bends on itself and forms a paraboloid in order to make up for the loss in circumference. Initial investigation involved the replication of such system and multiplying the modules which are then interlocked into each other to create various origami sculptures.

Circular Modules

Circular Modules

The system is then digitally simulated in order to extract the parameters which may affect the resultant geometry of the surface. With a combination of Kangaroo Physics, Hinge Forces and Springs, the digital simulation is created which allows anchor points to be placed, thus dragging for surface into various forms. Tests are carried out on different surfaces, including a closed circle of equal concentric rings, a closed circle of increasing concentric rings as well as an open circular strip with concentric rings. With an increasing fold angle, the bend angle increases.

System Exploration

System Exploration2

System Exploration

System Exploration

Upon cutting the closed circle, the surface becomes an open ended circular strip. The constraints that follow a closed surface no longer presents itself, thus allowing the strip to bend freely – although the principles of the system still applies. With increasing fold angles, the strip bends at greater angle. Having this revelation, different open ended strips are then tested against different parameters to extract the system further.

Parameters

Parameters

Parameters

Parameters

Parameters

In parallel to the research of curved crease folding is the investigation into the probability of transferring the system onto a more rigid, larger material, such as plywood. Here lattice hinge / kerf folds are employed, allowing the plywood to bend in a similar manner to card and paper. The final patterns for the hinges are a result of rigorous testing through trial and error. By repeating the modules we begin to see that, due to the folds, plywood can be as flexible as card.

Lattice

Lattice

First developed in 1979 by Dániel Erdély the Spidron is created by recursively dividing a 2-dimensional hexagon into triangles, forming a pattern that consists of one equilateral followed by one isosceles triangle. The resulting form is of six Spidron legs that, when folded along their edges, deform to create a 3-dimensional Spidron.

Spidron Nest

Spidron System_Parametrics_Lorna Jackson

Initial investigations into the Spidron system using paper resulted in irregular shapes that could not be predicted, and therefore replicated precisely. Progressing onto using rigid materials allowed the system to be broken down into six components, removing unnecessary triangulated fold lines, and developing latch folded Spidron that is precisely the same as that formed parametrically.

Spidron System_Three SPidrons_Lorna Jackson

This relationship between parametric and physical tests of component based Spidrons in both regular and irregular hexagons, as well as various other equal-sided shapes, has enabled the development of large scale models concluding thus far in a 1:2 scale version being built which will continue to be developed as a pavilion for submission to the Burning Man festival.

In parallel there has been an investigation into the system at a smaller scale allowing for the Spidron nest to be made as one component. In order to achieve the 3-dimensional Spidron form lattice hinges, also known as kerf folds, have been employed. Rigorous testing into the best cutting pattern have resulted in a straight line cutting pattern that allows for bending on multiple axis at once.

Developing this smaller scale system for submission to Buro Happold the intention is to create an arrayed system that is a conglomeration of both regular and irregular spidrons with varying depths and apertures that are able to integrate various display models etc. within.

Toby Burgess and I are very happy to announce that HAYAM – Temple to Sunlight, designed by Josh Haywood of Diploma Studio 10, University of Westminster, has won the Burning Man Art Grant. Similarly to last year’s amazing experience building Shipwreck and Fractal Cult, we will develop the project with the help of engineers at Ramboll Computational Design and will travel to Burning Man in August to realize the project. Josh Haywood has just sent the great pictures below of the latest prototypes in which we are lashing the plywood pieces together.

 

Josh Haywood - WeWantToLearn.net - Hayam, Temple to Sunshine for Burning Man 2014

Josh Haywood – WeWantToLearn.net – Hayam, Temple to Sunlight for Burning Man 2014

Josh Haywood - WeWantToLearn.net - Hayam, Temple to Sunshine for Burning Man 2014

Josh Haywood – WeWantToLearn.net – Hayam, Temple to Sunlight for Burning Man 2014

Josh Haywood - WeWantToLearn.net - Hayam, Temple to Sunshine for Burning Man 2014

Josh Haywood – WeWantToLearn.net – Hayam, Temple to Sunlight for Burning Man 2014

Josh Haywood - WeWantToLearn.net - Hayam, Temple to Sunshine for Burning Man 2014

Josh Haywood – WeWantToLearn.net – Hayam, Temple to Sunlight for Burning Man 2014

Toby and I explain the reason behind these projects in the TedX video below, The Architecture of Joy:

 

As the grant is limited, we need your help to pay for transportation and the additional costs related to construction, you can donate on the PayPal button below:

Happy new year! We are back and had our first tutorials session today. Students are submitting their portfolio on Tuesday and have started the last brief (see all our briefs for the year here). Here are two projects which are worth sharing for the following reasons:

  • Ieva Ciocyte’s elevation and plan drawings are very clear, with attention to details: traced Burning Man people, perfect shadows and lineweights, labels and dimensions. It just looks good.
  • Andrei Jipa manipulated the G-Code of his 3D Prints to create a continuous extrusion. Instead of slicing the prints horizontally, he generated a print path that follows the geometry and goes up in a spiral.

More beautiful projects on Tuesday evening!

Elevation 1 - Ieva Ciocyte Interlocking Plywood Tower

Elevation  1  – Ieva Ciocyte Interlocking Plywood Components Tower

Elevation 1 - Ieva Ciocyte Interlocking Plywood Tower

Elevation 2 – Ieva Ciocyte Interlocking Plywood Components Tower

Plan - Ieva Ciocyte Interlocking Plywood Tower

Plan – Ieva Ciocyte Interlocking Plywood Components Tower

Andrei Jippa's 3D printed intersecting component - Strange Attractors

Andrei Jipa’s 3D printed intersecting components made from a custom G-Code and used for his Strange Attractors pavilion

Andrei Jippa's 3D printed intersecting component - Strange Attractors

Andrei Jipa’s 3D printed intersecting components made from a custom G-Code and used for his Strange Attractors pavilion

Andrei Jippa's 3D printed intersecting component - Strange Attractors

Andrei Jipa’s 3D printed intersecting components made from a custom G-Code and used for his Strange Attractors pavilion

We just finished our last tutorials of the first term! Congratulations to all the students for the great three months and looking forward to the remaining two terms.

Students completed both briefs (brief01:systems and brief2A:festival) and are starting the case studies of events as part of our last brief (brief2B:realise).

Here are couple pictures of the projects we have seen during the last tutorials. Where do you suggest building the structures over the summer?

Merry Christmas & best wishes for the New Year!!

John Konings's towering gridshell.

John Konings’s towering gridshell.

John Konings's towering gridshell.

John Konings’s towering gridshell.

John Konings's towering gridshell.

John Konings’s towering gridshell.

Andres Jippa's 3D prints, driven by Chaos theory's strange attractors.

Andres Jippa’s 3D prints, driven by Chaos theory’s strange attractors.

Andres Jippa's 3D prints, driven by Chaos theory's strange attractors.

Andres Jippa’s 3D prints, driven by Chaos theory’s strange attractors.

Andres Jippa's 3D prints, driven by Chaos theory's strange attractors.

Andres Jippa’s 3D prints, driven by Chaos theory’s strange attractors.

Andres Jippa's 3D prints, driven by Chaos theory's strange attractors.

Andres Jippa’s 3D prints, driven by Chaos theory’s strange attractors.

Andres Jippa's 3D prints, driven by Chaos theory's strange attractors.

Andres Jippa’s 3D prints, driven by Chaos theory’s strange attractors.

Andres Jippa's 3D prints, driven by Chaos theory's strange attractors. Construction Component.

Andres Jippa’s 3D prints, driven by Chaos theory’s strange attractors. Construction Component.

Henry Turner's Curved Intersecting Plywood Wave Structure

Henry Turner’s Curved Intersecting Plywood Wave Structure

Ieva Ciocyte's Flame Tower made of Intersecting plywood components

Ieva Ciocyte’s Flame Tower made of Intersecting plywood components

Sarah Shuttleworth's Moebius Strips made of Steel Stars.

Sarah Shuttleworth’s Moebius Strips made of Steel Stars.

William Garforth-Bless' Bamboo Hammock Amphitheatre

William Garforth-Bless’ Bamboo Hammock Amphitheatre

William Garforth-Bless' Bamboo Hammock Amphitheatre

William Garforth-Bless’ Bamboo Hammock Amphitheatre

Very enjoyable crit day for DS10 at Westminster University. It was our second cross-crit of the year and students showed their proposal for Brief2A, building an interactive structure for Burning Man or the festival of their choice.

Thank you very much to our helpful crits Harri Lewis (Ramboll RCD our engineers for last year’s Shipwreck and Fractal Cult), Marie-Isabel de Monseignat (Tutor at DRS1 Chelsea College of Art), Dusan Decermic, Anthony Boulanger and Katherine Herron. Here are couple pictures:

Marie de Monseignat is holding the Plywood Spiralohedrons

Marie de Monseignat is holding the Plywood Spiralohedrons

Jessica Beagleman's Plywood Spiralohedrons

Jessica Beagleman’s Plywood Spiralohedrons

Sarah Shuttleworth's large metal origami model.

Sarah Shuttleworth’s large metal origami model.

Paul Thorpe's Twisting Plywood pods 1:1 Model

Paul Thorpe’s Twisting Plywood pods 1:1 Model

Ieva Ciocyte's Burning Euclid Wall

Ieva Ciocyte’s Burning Euclid Wall

Joe Leach's Burning Seed Reciprocal Structure

Joe Leach’s Burning Seed Reciprocal Structure

Sarah Stell's wind powered animals

Sarah Stell’s wind powered animals

Josh Haywood's beautiful Digital Muqarnas

Josh Haywood’s beautiful Digital Muqarnas

Henry Turner's intersecting plywood wave structure.

Henry Turner’s intersecting plywood wave structure.

Will Garforth-Bless' bamboo and fabric hypars

Will Garforth-Bless’ bamboo and fabric hypars

Lorna Jackson's Spacer Fabric Cloud

Lorna Jackson’s Spacer Fabric Cloud

Charlotte Yates' Origami Roofs

Charlotte Yates’ Origami Roofs

Naomi Danos' Folding roofs.

Naomi Danos’ Folding roofs.

Mark Simpson's mirror diamonds in the desert.

Mark Simpson’s mirror diamonds in the desert.