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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:

 

 

 

 

   Triply Periodic Minimal Surfaces

  Minimal surface is an area minimizing surface whose mean curvature at any point is zero, and is often represented by the shapes of soap bubbles that span wire frames. Some minimal surfaces have crystalline structures that repeat themselves periodically in three dimensions. Many of these surfaces were discovered by Alan Schoen who analysed them in his technical report, ‘Infinite Periodic Minimal Surfaces without Self-Intersection‘, written in 1970. I first started researching the different types of triply periodic minimal surfaces to understand the rules behind their structures.

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Schwarz Surface

Neovius Surface

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Lidinoid Surface

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Gyroid Surface

 Folded Hyperbolic Paraboloid

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Parametric Kerf Bending

I have also been investigating different types of lattice hinges or cutting patterns that could help fold a hyperbolic paraboloid from a rigid single sheet material.

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inversion_2

The Inversion Principle is a mathematical formula that maps points from inside to outside a circle and vice versa, governed by the equation MQ = r2/MP where [MP] is the distance between the origin of the circle and a chosen point and [r] is the radius of the circle. The chosen point is then moved along motion vector [MP] at new distance [MQ].

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Initial experiments explored inverting a series of two dimensional shapes through a circle. Each shape or series of curves was first divided into a series of points which were remapped using the inversion principle and then reconnected with the same relationship.

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The same process can be applied to three dimensional objects, using a sphere as the inverting object as opposed to a circle. Below is the inversion of an Icosahedron, achieved by dividing the initial shape into a series of vertices defining the faces. These are remapped by the Inversion Principle and then reconnected with the same relationship to give new vertices and faces.

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Exploration into the number of subdivisions showed that the more vertices a shape is divided into, the more it approaches its ‘true’ approximation. Less subdivisions leads to a more faceted output geometry.

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These experiments were followed by a series of physical models which investigated modelling the interior volumes of the 3D object as a series of two dimensional planes using both spheres and cylinders as the inversion object. Below are the internal volumes of an inverted Dipyramid and four sided pyramid.

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We are pleased to announce that DS10 student Andrei Jipa has been nominated for the RIBA Silver Medal 2014, for the best part II student project in the UK.

Andrei’s futuristic proposal “Solanopolis” blended a radical futuristic vision with an advanced understanding of mathematics and 3D printing technologies to create a 3D printed city whose design sprang directly from the underlying code in fractals, creating stunning architecture which echoes the implicit mathematical beauty found in Baroque architecture.

In order to physically recreate these proposals Andrei pushed the boundaries of 3D printing, rewriting the code sent to the 3D printer, devising and publicly sharing a new way of 3d printing with the world.

This was all set against a fantastically creative post apocalyptic narrative of an entire culture and economy based around growing potatoes and turning potato starch into plastic for an army of large scale 3d printers to keep on building up from the rising waters of a future flooded world.

It was in our opinion a very creative blending of brave ideas backed up by rigorous technical research and real world physical results, and we think he has a great chance of winning this years prestigious prize.

Andrei’s proposal will be featured soon on the RIBA website http://www.presidentsmedals.com/

Farm Section~  004s 001s

But wait, there’s more! On top of that yet another DS10 project, Hayam Temple designed by Josh Haywood, has been built over the Summer by a team including past and present DS10 students and  is currently bringing joy to the revellers at this year’s Burning Man festival in Nevada and has been receiving praise all over the place.

The beautiful project inspired by the delicate muqarnas found in Islamic architecture has received great international praise and has been featured across the web…

http://www.dezeen.com/2014/07/02/hayam-temple-by-josh-haywood-for-burning-man-festival/

http://www.huffingtonpost.com/2014/07/30/burning-man-2014-art_n_5632531.html

http://inhabitat.com/josh-haywood-designs-stunning-lasercut-plywood-pavilion-for-burning-man-festival/

10608431_532651670195593_877742028231652468_otemple2temple11Me and Arthur are greatly looking forward to yet another year of exciting designs and joyful architecture at Westminster University and very excited about the year ahead 🙂

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

We are now on Kickstarter! Click on the image below or on this LINK to kindly back our projects.

Swing-Kickstarter-logo

Little summary of our productive day at Westminster with Chris Ingram and Georgia Collard-Watson: We produced a 1:1 physical model of the wood laminate technique recommended by Ramboll (drawing shown in previous post). We will us this technique to form the twisting longitudinal spines on our building.

The openings on the back ribs are now defined parametrically by a sine curve and unroll with the strips for fabrication.We tested couple options and are happy with the one shown below which breaks the direction of the strips.

Working on the parametric model with Chris Ingram at Westminster University

Working on the parametric model with Chris Ingram at Westminster University

Georgia Collard-Watson with the 1:1 laminate prototype

Georgia Collard-Watson with the 1:1 laminate prototype

Chris Ingram testing the bendiness of the laminate structure

Chris Ingram testing the bendiness of the laminate structure

Testing the notches

Testing the notches

Resolving Shipwreck's structure - Working on the interface between back stripes and vertical ribs.

Resolving Shipwreck’s structure – Working on the interface between back stripes and vertical ribs.

Resolving Shipwreck's structure - Working on the interface between back stripes and vertical ribs.

Resolving Shipwreck’s structure – Working on the interface between back stripes and vertical ribs.

Modelling the ribs and notches - We are currently adapting the ribs and spine to add strength.

Modelling the ribs and notches – We are currently adapting the ribs and spine to add strength.

The Sine curve Interface controlling the back strips openings on Grasshopper

The Sine curve Interface controlling the back strips openings on Grasshopper

The back strips openings

The back strips openings