Transforming Polyhedra

Spaces that can transform have important potential for architecture and building design, weather it is for logistical reasons (transporting buildings as a smaller volume) or for operational uses (if the building needs to expand to open and shrink to close, for example).

We have been experimenting with different types of transforming polyhedra at Architecture for Kids, looking at the Jitterbug, Hoberman structures, Juno Spinners and others.   In addition to any Architectural value, creating mechanical moving structures has proven a lot of fun.

Experimenting with transforming polyhedra

Jitterbug
A discovery attributed to Buckminster Fuller, transforms between octahedron and cub-octahedron. It also demonstrates to kids the inherent structure found in triangular shapes, and how this lack of structure in the quadrangle can be used to the advantage of the Jitterbug's articulation.

We have been assembling Jitterbug's using modular origami.

A quickly constructed origami jitterbug

Hoberman Structures
We love the Hoberman Sphere!  It's always great fun in class. The immediate attraction is that an operation to one joint affects the whole model. Different Hoberman spheres work with different members of the Archimedean Solids which has increased class interest in polyhedra, their differences and how they work. 

Polyhedra-head: Playing with the Hoberman Sphere
and framed structures.

Expand-a-ball similar to the Hoberman Twist-O

Juno's Spinners
My favourite, Juno's Spinners were developed by Junichi Yananose.  They are polyhedra held together with an internal structure which also acts as a mechanism to allow them to expand. Rotational joints at the junctions between the structure and panels allow this movement, and like the Jitterbug and Hoberman Structutes, the model expands and contracts uniformly. 

Making Juno Spinners

At first they look complicated, (they are ingenious) but the templates are available on Juno's website and they are straight forward to template, cut out and assemble. We've been using polycarbonate sheet with eyelets for the joints. For most models no real instructions are required because the geometry constructs itself. 

These are useful exercises to de-mistily geometry and the apparent complexity of movement. It is also good to help develop kid's motor skills with the tracing, cutting, folding and assembly involved, but these tasks don't take long and the goals of finished models are quickly realised.

Drawing in Space

I'm sure Alexander Calder would have taken to 3D pens if they had been available. His wire sculptures of faces and figures and experiments in 'drawing in space' might have been a lot quicker to produce and resulted in many more studies.

From the Calder review in Culture Whisper

But for kids, artists and architects today they are a very useful resource for creating sculptures and spacial studies quickly, to capture ideas and demonstrate skills in 3D thinking. 

Instinctively working in 2D

To begin with it does take a little practice and thought. When used by kids for the first time, they often set out their work on a flat sheet of paper and replicate a single 2D design. This produces a result but might not have the depth of character as a 3D line sculpture, which takes on a new life when seen using shadows, like Calder's work. 

Trying to replicate 'drawing in space'.

Creating the design in a number of parts, using a flat paper surface to create a series of single curve components, allows the overall piece to be constructed into a 3D assembly which is closer to what Calder was trying to do. We could all be great artists! 

A family of sculptural heads

It demonstrates how the simplicity of the line is a such a powerful tool for representing an idea, provoking thought or raising a reaction. 

Flexible Building Skins

Adventures in 3D printing highlight several valuable examples of surfaces which accommodate double curve geometries and can even transform to create flexible skin-like surfaces.  The possibilities of these are exciting and should be of interest when considering Architecture's futuristic aspirations for moving, transforming or shape-shifting building structures.  Here are some examples of prototype flexible skins, available to print, test and experiment with:

Flexible Skins
Mesostructured Cellular Materials:  3D printed structures with the ability to deform and deflect in multiple directions as a result of their structural and geometric arrangement.

Mesostructured cellular sheet by Andreas Bastian
On Thingiverse  and his blog site

These examples by Andreas Bastian, with other examples of double curve geometries below:

Andrea's other experiments include cellular structural geometries with 3D printing, post-formed over double curve geometries.  These also offer an insight in to how double curve skins could evolve.

Delft University is always a hub of innovation.  These student experiments have led to similar positive results:

Flexible materials developed by Students at Delft University.

Stereolithographic fabrics: There are a variety of examples of stereolithographic fabrics produced through 3D printing.

3D printed fabric developed for clothing by Richard Beckett

Chainmail: An old invention made a lot simpler to produce with 3D printing.  Geometric variations and additions to the units such as scales or feathers add to the possibilities of the material.

Chainmail by Kacie Hultgren.  Square geometry used.

Scale mail armour by Tom West.
Scales could offer some weather resistance in a building application.
Closest I've seen to replicating shark skin with flexible double curved geometries.

Hexchain: A variation on the above using tessellating shapes with mechanical flexibility to adapt to double curve surfaces.

Hex Chain from Jay Jeon.  A variation on scale mail.  

Flex Mesh: A kit of parts with mechanical flexibility between the components to allow movement and tolerance in three dimensions.

Flex Mesh uses flexible components with different geometries to achieve flexible 3D surfaces

Fashion
3D printing is leading the way in fashion with developments to produce materials with mechanical flexibility to replicate fabrics.

3D printed fabrics by Iris van Herpen.  

Flexible fabrics exhibited at the NYC 3D Print Show.

Mechanically jointed geometric structures to create a flexible fabric by Kinematics

Kinematics Petal fabric

Footwear

3D printed trainers are on their way from Nike and Adidas, developed with 3D printing because of the potentially superior support and mechanical flexibility which this manufacturing method might offer.

3D printer trainers coming from Nike and Adidas

Accessories
3D printed clutch using rectilinear chain mail shown above. 

Clutch by Kacie Hultrgen

3D printing is drawing a lot of interest in architecture and building design, but that doesn't mean that building types need to be the same rigid structures or that site processes and prefabrication methods need to follow established patterns. It is useful to look beyond the building industry, into other areas of design and manufacture to see what neat ideas are with developing an a different scale.  Maybe one day buildings might be flexible with the ablity to move and transform as Ron Herron imagined. 

A load of old balls

Looking at the development of double curve geometries in building materials I was drawn to the design of sports balls and in particular footballs to see where developments in this area can inform building structures and architecture, as a source of inspiration and reference.  Materials, geometries and fabrication processes have developed to enable the products to be accurately made and perform under specific structural loads and performance criteria.

Relating to the Building Industry
From a building point of view, the sheets of material which make up the ball's outer skin might equate to prefabricated building panels and some key difficulties remain in creating double curved panels which are:

• Achieving the optimal size of the panels or components within the restrictions of manufacturing, logistical and site handling constraints,
• Details of the junctions between panels including accuracy of fit and position, especially where multiple panels meet at corners, or where junctions are required to meet accurately along complexed curved edges,
• Sheets can often curve in one direction but curves in two directions without the special preparation or a mould is often difficult, 
• Being able to achieve the desired design with a controlled set of geometries.  Creating multiple double curve moulds adds significant cost to a project.

Curved building materials and issues of logistics,
accuracy of fit, weather tightness and prefabrication

Football Ball Design
The evolution of the design of the football has addressed some of these issues and offers parallels.  Looking at how the product has been optimised over time suggests a few tricks which might work for the structural envelopes of buildings.  For example:

c.1937 Football design 

Traditional football consists of:

• 18 panels,
• 32 three-panel junctions,
• 48 linear seams

Use of linear strips of materials to make larger double curved panels.  Strips bend in one direction, with the seamed panels creating the curve in the second direction.  Six of the larger panel arrangements work like a rounded cube - set around an x, y, z, (three) axis arrangement.

1963 Adidas Santiago World Cup Ball

1963 Santiago Ball consists of:

• 18 panels, of which 6 are octagons and 12 are symmetrical polygons,
• 40 three-panel junctions,
• 58 linear seams

Arranged with a greater understanding of spherical geometries but still based around an x, y, z (three) axis arrangement.

1970 Adidas Telstar World Cup Ball

1970 Adidas Telstar Ball consists of:

• 32 panels, 20 of which are hexagons and 12 are pentagons, 
• 58 three-panel junctions
• 90 equal linear straight seams

Based on the truncated icosahedron, one of the Archimedean polyhedra, also known as the Bucky ball or carbon 60 atom.  Probably the first ball design which adopts more complex three dimensional geometric design.  The pentagons align with six axis rather than three as used before.  The quantities of panels, seams and junctions make it relatively more complicated than the others.

2006 Adidas Teamgeist World Cup ball

2006 Adidas Teamgeist World Cup ball consists of:

• 18 panels of two types (6 of one and 8 of the second),
• 20 three-panel junctions,
• 36 seams, of which 24 are curved and 12 are straight.

The Telstar design has probably become the most common football ball design and has experienced a long design life, but more contemporary designs have investigated how the ball and its performance can be optimised with fewer components and junctions.  The Teamgeist  ball demonstrates this.  It also returns to a three-axis geometrical arrangement.

2010 Adidas Jabulani World Cup Ball

2010 Adidas Jabulani World Cup ball consists of:

• 8 panels of two types (4 of each type).  
• 12 three-panel junctions,
• 18 linear seams of which 12 are long and curved, 6 are short and straight. 

These panels are pre-moulded in to a double curved shape to assist precision of build and performance.  The ball's performance is assisted with an additional intermediate lining between the outer skin and the bladder.  There are less panels and junctions than the Telstar ball, and it is based around a four-axis geometry.

2013 Nike Ordem Premiership Ball

2013 Nike Ordem is based on a dodecahedron and consists of:

• 12 equal panels, each fabricated in to six sections which adapt to take on a double curved shape,
• 20 three-panel junctions,
• 30 straight linear seams.

A relatively simple design based on the dodecahedron.  The pentangle panels are articulated to create an effective double curve.  It might be seen as a simplified and optimised take on the Telstar ball design.  As with the Telstar ball the pentagons align a six-axis geometric arrangement.

2014 Adidas Brazuca World Cup Ball

2014 Adidas Brazuca World Cup ball design consists of:

• 6 equal cruciform panels,
• 8 three-panel junctions
• 12 curved linear seams

The cruciform panels are effective for curving down the long arms with the pressure of the bladder creating the second curve across their width.  The curved pattern of the seams meeting around a spherical geometry presents an assembly tolerance / accuracy of fit issue which looks dynamic but might prove difficult to achieve with building materials.  This ball returns to a three-axis geometric arrangement.

It doesn't always look the same when it comes through the post.
Junction alignment of panels around a double curve geometry.

A Load of Old Balls

A Load of Old Balls Simon Inglis

Simon Inglis's book A Load of Old Balls (2005) examines the development of the ball in British sports up to the twenty-first century and reveals much relevant information in relation to the development of materials, manufacturing processes, geometrical development and performance reliability.

On materials, it charts the greatest advances with the development of synthetic and composite materials to replace natural materials and animal parts.  It describes how material technologies from different industrial sectors were investigated to meet the requirements of the developing sports industries.  Mass production and standardisation allowed developments in ball design to progress with greater accuracy of manufacture and performance precision.  Even the 'crack' of the golf ball when hit by the driver is explained as a carefully engineered acoustic property.

Other Designs and Experiments

Haresh Lalvani's soccer ball

More recently Haresh Lalvani, Professor of Architecture at the Pratt Institute, has been experimenting with tessellating polygons which combine to create three dimensional spheres or ellipsoids.  His work is available to see at the Patents site.

Using intersecting cylinders set out around the axis of different platonic solids (cube 3-cylinders, tetrahedron 4-cylinders and dodecahedron 6-cylinders) allows surfaces to come close to double curve geometries, using single curve planes.

The cockpit roof lights for the Central Module at Halley VI
designed with the idea of intersecting cylinders
as an economy over double-curved glass

Examples in Buildings

Examples of double curved geometries in building materials are mostly seen with timber, concrete, glass, perspex, metal and FRP:

Achieving double curved geometries with building materials

How to Bring Architecture Fun into the Classroom

Experimenting with Architectural Design offers some intriguing lines of investigation for work in the classroom, so much so that the children don't see it as work, but more as fun.  Thanks to Innovate My School for publishing our article in their online magazine today:

As part of their Art curriculum, Furzedown Primary School in South West London has been running workshops on Architectural Design.  This is to help the children's’ knowledge and understanding of materials, structure, colour and aesthetics, and how they can be applied physically into built assemblies.  Architectural design is not a subject normally taught in schools before college, but it is a subject that is very relevant to everyone.  We all live in the built environment which is heavily managed with lots of design interventions.  Individually and collectively these affect us directly, so why not bring architectural design in to the classroom?

This is what they have been doing:

Experiments with structure

The children have been learning about structures in nature and man-made objects, and understanding how some applications found in nature have been applied to the engineered products we use today.  Forces and their applications were explained and some unconventional structural solutions were also examined.

Structures in nature, products and architecture

The children were given sets of construction toys with challenges to create the tallest, largest or longest spanning structure, to put some of the theory to the test.  It is when they were hands-on with the kits that value of structural triangles over conventional squares and rectangles really became apparent.

Experimenting with structural toys and kits

Experiments in drawing

Graphically representing your design proposals in a format that can be universally read is a bit of a skill.  Class lessons looked at plans, sections and elevations, and how they could be used to construct a 3D axonometric. 

Representing design with drawings, images and concept models

Challenges for the children included tasks ranging from ‘draw your ideal room’ to ‘design a fantastic building of the future’.  Their imaginations did not let their work down and the confidently produced results were full of drawn articulation and annotation to describe the proposals.

Putting down ideas in 3D with axonometric paper

Architectural design and model making

An introduction to architectural design looked at materials, colour, light transparency, form and how different types of spaces might affect how we feel.

Some design considerations

A range of freely available materials was gathered for making models with.  This included cardboard tubes and sheets, string, pipe cleaners and scooby-string, coloured translucent plastic film and lollypop sticks etc.  With their recent understanding of how structures perform and ideas of spaces, the children set to work inventing prototypes for an installation of their choice for the school playground.  Ideas ranged from places to hang out with friends in to sculptural designs, to activity spaces.

Experimenting with design

Adventures in building

The series of lessons gave enough time to trial the assembly of one of the prototype designs.  This was a bit of a risk because things that work in model form often behave differently when scaled up.  The selection of materials had been planned so that everything used for the prototypes had a corresponding larger version for a full-size assembly.  Cardboard tubes and sheets transferred to carpet roll tubes and estate agent boards, string became rope and coloured ribbon became fabric strips etc.

Making structures on a larger scale

The prototype selected became the ‘Random Funky Festival Pavilion’ and a place where much of year 5 could sit and eat their lunch at and debate important matters at break time.

The Random Funky Festival Pavilion designed and built by class 5S

 Skills learnt

As well as mentally gaining an understanding on how structure and design works through listening and applying, the children also practiced activities which helped with their motor skills.  The making of both small and large structures challenged their cutting, making and assembly skills.  As part of the design work the children investigated folded card structures and modular origami, which took some time and attention to master. 

To this end, I am confident that the series of lessons into architectural design helped the children to progress in line with the School’s aspirations for learning development.  Hopefully it opened their imaginations to a new area of design exploration and built confidence.  The work was also designed to complement the National Curriculum in England for design and technology programmes of study, which calls for a process of designing and making using a set of skills based around maths, science, engineering, computing and art. 

Related articles:

Architecture for kids

Monocoque structures for kids

Team building with boards

Space to let – in a mobile den

Designing pavilions