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Drawings

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.

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`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:

 

 

 

 

 

An exploration of the simplest Hyperbolic Paraboloidic ‘saddle’ form has lead to the development of a modular system that combines the principles of the hypar (Hyperbolic Paraboloid) and elastic potential energy.

A hyperbolic paraboloid is an infinite doubly ruled surface in three dimensions with hyperbolic and parabolic cross-sections. It can be parametrized using the following equations:

Mathematical:   z = x2 – yor  x = y z

Parametric:   x(u,v)=u   y(u,v)=v   z(u,v)=uv

The physical manifestation of the above equations can be achieved by constructing a square and forcing the surface area to minimalise by introducing cross bracing that has shorter lengths than the  square edges.

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A particular square hypar defined by b = n * √2 (b=boundary, n=initial geometry or ‘cross bracing’) thus constricting the four points to the corners of a cube leads to interesting tessellations in three dimensions.

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Using a simple elastic lashing system to construct a hypar module binds all intersections together whilst allowing rotational movement. The rotational movement at any given intersection is proportionally distributed to all others. This combined with the elasticity of the joints means that the module has elastic potential energy (spring-like properties) therefore an array of many modules can adopt the same elastic properties.

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The system can be scaled, shaped, locked and adapted to suit programmatic requirements.

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A geometric wall of fire burning on the sands of the Black Rock Desert. This immobile blaze stands as an edifice to Burning Man’s original figurehead. A burning yet fireless wall of plywood and acetate that can be encountered, entered and sheltered in.

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This sculpture stands as an abstract image of flames sent by Vulcan the Roman God of fire, an emblem of the festival’s name. Created from a series of plywood shapes and acrylic, Vulcan’s Flame is a blazing wall of light and colour. The structure is created to both imitate and juxtapose chemical fire, sharing real fires beauty but opposing its destructive tendencies. The sculpture is designed as a wall of shelter, behind which burners can be shielded from the desert’s unforgiving sun.

Born from Ancient Egyptian ‘Cairo tiling’, the sculpture is created from morphing polyhedra. The lowest section of the fire is created from cubes which gradually deform into rhombic dodecahedrons – a cubist interpretation of a flames movement. Internally every shape is painted to mimic fire’s bright hues and coloured acetate panels within the wall will project red and yellow tones onto the surrounding desert floor. At night internal spotlights will illuminate the entire structure, creating a glowing inferno of colour. These lights will flicker to create the illusion of movement.

Visually the main structure consists of three main forms;

  • The outer zone: the sparse cubic section of the sculpture, representing the hottest part of a flame, the region of complete combustion
  • The middle zone: this is the central area in which the cubic deformation begins to occur.
  • The inner zone: this is the coolest space, the most densely packed red area of the sculpture. Burners can crawl into this space – sheltered by four layers of dodecahedrons.

Rendered Plan

Physical Description:

Vulcan’s Flame is a long, low plywood structure, the installation is the geometric interpretation of a flame, a curving sculpture of deforming polyhedral that slowly transform from a cube to a rhombic dodecahedron. The sculpture is created from 55 plywood polyhedra constructed from hand cut plywood boards and secured with cable ties. Internally each shape is painted using natural, organic paints, as the shapes change their internal colour alters from yellow to red. Coloured acetate panels in the uppermost faces of each shape will mirror the shapes internal hue, these panels will allow sunlight through during the day casting beautiful coloured shadows on the desert floor. At night the sculpture will be lit internally with fluctuating spot lights, this will create the illusion of flickering movement. The acetate panels will be secured with nails.

Construction Sequence

The structure sits on a base of 23 plywood shapes, secured to the ground with rebar stakes. The sculpture is very stable as the base is the widest section, the rest of the sculpture tapers away towards the top. Each new shape rest on the 4 corners of the shapes below, bolted through the vertices and then secured with rope. The final and highest rhombic dodecahedron is stabilised with a steel column. The highest point on the entire structure is just over 11 feet above ground level and consists of 4 stacked shapes. A full sized version of one of the shapes has already been constructed and load tested confirming that it can support human weight, all of the cable ties securing the structure will be meticulously rubbed down to ensure they are not sharp.

The sculpture curves in a gentle arc – creating a central area of shelter from the wind and sun. At ground level Burners can crawl inside the structure and rest in it’s shady, tinted interior.


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Inspired by previous research of pyritohedrons, these structures are an addition to a series of other models based on polyhedral deformation. Previous models have experimented with density, altering colour and infill panels.

Previous Models

Philosophical Statement:

Inti: The Incan Sun God, his face portrayed as a gold disk from which rays and flames extended. Inti is the Sun and controls all that implies: warmth, light and sunshine. During the festival of Inti Ramyi, held during the Summer Solstice, Inti is celebrated with much drinking, singing and dancing - special statues are made of wood are burned at the end of the festival. This sculpture is an extended physical manifestation of this; decadent ritualism and a spiritual experience.

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Inti incorporates 288 petals are self-assembled into 12 concentric rings, with each petal representing the hours of the day and each ring every month of the year. These are held together using mirror polished circular brackets, designed to catch the light and reflect circles of sunlight around the structure interior. Inti's focus is the sunrise; as the sun rises on the playa, Inti is designed to catch the light at this precise moment and funnel through the piece, enveloping and bathing the burners inside with it's warmth and spirit.

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01 Day

Philosophical Statement:

‘Timber-Wave’; a plywood instillation emerging and crashing on to the desolate Black Rock Desert. This breaking wave a remnant of the retreating Quinn River, draws on imagery of both waves and dunes provoking thoughts of the original Burning Man Beach Parties and surfing counter culture. Simultaneously the design evokes concepts of the Silk Road as a mirage of a giant wave appearing from across the playa to be discover by wondering burners.

The design of the Timber Wave was driven by creating an interactive environment. In daytime, people are encourages to climb and search between the interwoven plywood structure. Open sun soaked communal areas create areas for group contemplation. Solitary areas for single travelers have also been designed as places of refuge from the intense sun, wind and dust storms hoping to encourage serendipity. At night the wave truly come alive as a monument to the sea. Bathed in varying blue tones of color the spectacular structure is a mysterious beacon within the dark playa.

02 Night

Physical Statement:

‘Timber-Wave’  structure consists of 3 layers of 12 intersecting plywood ribbons.  Each ribbon consists of a varying number of water bent plywood components con-caving and con-vexing together forming a rigid series of tensioned and compressed sections.  The result is a homogeneous structure creating a beautiful ergonomically sized spaces. Each ribbon a series of circular penetrations in the form of an abstracted water pattern.  Creating foot and hand holes for climbing as well as allowing dramatic shadows to be cast throughout the structure and across the playa. At night the penetrations allow the lighting of the instillation to spill across the playa and between the layers of the structure.

03 Day

04 Internal Image

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1:20 Scale Model

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Link: issuu.com/henryturner/docs/portfolio?e=0/6863548

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Narrative | ‘Orbit’, an aluminium tube pavilion stands as a playful take on the orbit of our solar system. A kinetic, inhabitable architectural structure that orbits around itself revealing a central, occupiable space that acts as a ‘center of the universe’  location within which the occupier will experience the rest of the world rotate around them.

Occupiers act as planets orbiting around one another, taking in the beautiful surroundings as each hammock level gently rotates as if it is floating, free from visible connections below, In order to reach these relaxing levels, the occupiers must scale its lightweight structure eventually reaching the central ‘ritualistic’ epicenter.

Physical Description | Orbit stands as a playfully abstract vision of the universes orbit around the sun. Visually the structure is very simple. A series of single recursively scaled down forms provide both the frame work in which to house multiple levels of hammock space to relax whilst also offering a highly structural climbing frame that is scaled in order to reach its epicentre.  It stands tall amongst its neighbours as a combination of both inhabitable architecture and a visually striking art piece.

The structure is composed of multiple interlocking aluminium tubes of varying diameter that hang from a single point supported by the main outer structural framework.  Within the opening at the bottom of each frame is space for hammock netting to be fitted to the aluminium tubing providing an inhabitable space to relax on.

The inset neon LED lighting on the inside of the aluminium tube frame enhances the proposals visual impact at night, illuminating to be seen from near and afar.

Interactivity | There are multiple levels for potential seating, each incorporating a hammock like mesh suspended between the aluminium structure. This provides a comfortable place to relax whilst the structure gently rotates about its axis. As with most exciting Burning Man installations, this structure is climbable with the final point to reach being the central frame large enough for one person to sit in whilst the rest of the structure rotates around them.

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Focus_Day RenderBurning Man Art Instalation Proposal

Focus when assembled would be a material artifact, approximately 8-9meters height tower, triangular plan with the central focal point, where is the place for the fire.

The tower envelope consists of three walls that form a continuous surface. Wall construction should follow a simple process, adding rows of intersecting components one after another, starting from the base until the last row.

The design of Focus started by looking into a mathematical system of an Euclid’s algorithm and it was a way to generate it’s constituent elements, but it didn’t define the final physical form. The mathematical expression was left at some point during the creative process, when it was found as a formalized system that is closed and univocal and does not contain qualities of the artwork.

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Although this artwork started as a mathematical formula, which was a rational and ideal expression intended for the rational and conceptual human being. Later Focus became a work of art when an intention of it was to be understandable and perceivable to all, this was achieved by mixing sensible matter and form of mathematical symbols with conceptual content.

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Focus physical model2

Focus expresses itself in its own name and name holds its meaning. The name Focus has multiple meanings as the art work will always have embedded message given by the artist, but at the same time it is not necessary to know the story behind it. It will have a meaning that participants would give to it themselves. In Latin, the word Focus means hearth, fireplace, center of interest or activity, but it is not necessary to know the meaning to understand it. Focus would be a perceptive expression, as perception is the act and the result of the act, which consists through the senses and the mind.

Focus Interior Space

Focus would create strong sensual experiences for the participants and observers. It is designed to play with visual, tactile, aural experiences and perception of these qualities would bring a human being into play with his own entity.

Its purpose would be a matter of expression.  It would be at the service of nothing and no one, but at the same time it would exist to act on the human beings.

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Focus is the autonomous work for the autonomous human being who wanders around or goes inside to find what it holds, searching for the constitution of a meaning or, which amounts to the same, searching for ones own constitution.

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