## Bending Lattice System

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.

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.

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.

`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.

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.

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

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.

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.

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.

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:

## 4th May 2015 Tutorials

Hello everyone, here are couple pictures from our last tutorial showing some of the best future cities that our students are currently working on in response to the Brief03:FutureCities.

From an open-source green city living in symbiosis with the Amazonian forest to a terra-forming city on Mars made from 3d printing robots carrying giant Fresnel lenses all the way to a rent-for-advertisement growing infrastructure covered with LED screens – we are look forward to discovering with you the cities of tomorrow from our wonderful and creative DS10 students next Thursday at the Interim Crit.

## Reflection

Reflection presents this years burners with an intimate setting in which to share their inner most confessions, secrets and tales – With the option to do so both openly with other burners face to face, or retain the mystery of their identity by sharing with a complete stranger through the pavilions semi private screen. Reflection embodies the theme ‘Carnival of Mirrors’ in a variety of manners:- the geometry of the pavilion not only mirrors itself in its own form, but also incorporates a reflective surface within its interior spaces. The reflective physicality of the pavilion beautifully juxtaposes its function, by giving its burners a physical platform with which to cogitate their innermost thoughts and feelings, and share these with others. The pavilion is created as a result of rigorous testing of origami in order to create a single Spiralhedron which is then mirrored through along all axis.

Based upon a geometric origami principle which outlines the rules for the triangular subdivision of a 2-dimensional shape and assigns mountain and valleys creases to each subsequent subdivision the Spiralhedron has been optimised through both digital and physical testing. Reflection takes an abstract approach to this years theme, the pavilion’s form manifests itself as a result of mirroring this singular Spiralhedron in the X,Y and Z axis, which in turn creates its enclosing plywood form. In order to create the semi-private confessional screen, the panels incorporate a pattern, providing both the function of privacy, but also narrating the origins of the pavilions final form.

Construction

Due to form being created through the act of mirroring the entire pavilion will be made of 9 unique laser cut panels which will be bolted together with both metal hinges and 90 degrees and wooden brackets at 135 degrees.

Dimensions

Constrained by the size of a plywood sheet each individual Spiralhedron is made of two sheets of plywood (requiring 16 in total). Made of eight spiralhedrons ‘Reflection’ has a footprint of 3.5metres*3.5metres with a maximum height of 3.5m creating a footprint equal to that of the height of the pavilion.

## The Petal Hypothesis

The petal has long been a surround for the reproductive parts of the flower, its varied forms and designs attract numerous species of animals and insects, enabling its existence to grow and spread. As a result, the petal will not only encounter pollen of its own species, but also that of many differing plants.

Taking people as the pollen. This caravanserai will attract people both day and night, providing a space for play and discussion, encouraging communication, observation and interaction.The Petal Hypothesis sits expressively within its setting. Exposing the raw structure of the plywood ‘petals by day and revealing the elaborate display of the EL wires by night.

Configured in a circular array, each ‘petal’ is construct from just two ‘pods’ which in themself only take 1 sheet of plywood to construct. Connected together to generate one ‘2d’ curve, the end points then bend around to complete the monocoque structure.

These pods are then mirrored to generate the ‘petal’ form and anchored to the ground. The act of fixing the extreme widths and mirroring the pods minimises the natural flex within the ‘pod’ and enables it to be a strong physical structure.

In place of the EL wires, a cloth stress skin has been incorporated to the top tier of petals. This not only provides shading during the day but also absorbs the light from the EL wires and distributes it across the whole surface.

Interactivity:

Observe – Sit around and within the ‘petals’ to observe the activities at its centre.

Inhabit – Climb the structure and occupy one of the many vantage points within the ‘petals’

Connect – Share memories and congregate either on mass at its centre or privately within the petals

## Interim Portfolio Review

We just finished the interim portfolio review, students submitted their work so far in the form of a beautiful portfolio. We asked for 25 digital pages, Two beautiful A2+ prints, a working portfolio and an abstract. Here are some of the most complete portfolios we’ve seen:

## 16th January 2014 Tutorial

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!

## Updates on Burning Man – Fractal Cult and Shipwreck

Hello! Couple technical updates on our Burning Man Projects for the team, donators and potential collaborators:

• We have developed the structure, geometry and details of the two projects with the help of Ramboll Computational Design (RCD). See drawings and analysis below.
• We have signed the contract with Burning Man and received the first grant payment 20 of us are signed in to go.
• We have sent our first fabrication files to get an initial quote on CNC milling all the pieces on 2440mm x 1220mm exterior grade plywood sheets of 9mm (for Fractal Cult) and 3mm (For Shipwreck). Our hope is to collect the pieces on the 19th August.
• We will start small models to test the new structures
• The Shipwreck now has a parametric model which outputs all the cutting profiles.

You can also comment on this page to make suggestions on the fabrication – We need more quotes for the CNC and/or Laser cutting job in the U.S. West Coast (Los Angeles, San Francisco, Las Vegas, Sacramento, Fresno, Reno preferably) . We also need quotes for the scaffolding structure.

## Andrew Heumann’s Case Study in Translation

Wonderful thesis project of Andrew Heumann at Cornell University. Text extracted from his blog:

“Entitled “Case Study in Translation,” the project attempted a parametric reinterpretation of the Case Study House program of the American Mid-Century. Beginning with parametric analysis of the precedent houses, the project attempted to understand the formal and functional logics at work in the houses, and produce algorithmic translations of those logics in order to bring them into a contemporary context, adapting them for the cultural conditions of the present day.”

Couple drawings from the thesis:

Several videos from Andrew’s vimeo channel:

## FINAL PORTFOLIO REVIEW

The academic year is almost over, the graduation show and prize ceremony is in two weeks. Toby and I just assessed everyone’s portfolios with the help of other tutors from Westminster. This is a very stimulating day in which all the studios’ year-long student work is seen and its diversity revealed. Students could not be part of the process and witness the efforts and beauty of the some of the work so here it is, a little selection of some of our most creative portfolios this year:

## A Bio-Plastic temple in the Polymer Valley

After developing a series of experiments with bio-plastic made from potato starch, glycerine and vinegar, Marilu Valente created a digital form-finding technique which uses the same principles as the elastic material. Below is a plan of the resulting building, a bio-polymer centre in the Polymer Valley in Thelford, U.K. We will be updating this post soon but wanted you to see how a complex three-dimensional Architecture can still be communicated through a beautiful 2D plan.

#PotatoStarchIsTheFuture