Space Filling Polyhedra

Purely out of curiosity, this is a summary of all the space filling polyhedra; forms that tesselate in 3D.  It should cover the basic variety of forms but there are several additional variations from these which can be achieved by bisecting, elongating, twisting or distorting the basic units.  Some but definitely not all are noted here. 

Space Filling Polyhedra

The cube is the only platonic solid to tessellate in 3D.  The triakis truncated tetrahedron is the closest form to the tetrahedron.  Shapes which tessellate in 2D work as space filling polyhedra when extruded into prisms.  Slicing, bisecting and skewing these prisms create further space filling forms such as scutoids.  There are also other variations of gyrobifastigium, hendecahedra and hexahedra which form their own families of polyhedra.  The square based pyramid is a very versatile form for mediating between the cube,  rhombic dodecahedron, dodecahemioctahedron, elongated square pyramid and other forms.   More complicated geometries such as the plesiohedron and stephenoid hendecahedra accumulate into dynamic collections of forms.  All of this is worth an investigation in relation to architecture for its innovative value to create economical and dynamic spacial arrangements of buildings.

Are Buildings Affected by Wind Chill?

The wind chill effect is the temperature that a person feels because of the wind.

Air temperature feels colder combined with exposure to wind. 

It's a combination of the external temperature and wind speed.

For example, a bottle of water placed outside at 4ºC, exposed to the wind
will cool to the ambient temperature quicker than the same bottle placed in a fridge at 4ºC
(even with the fridge door closed).  

The temperature of water in the bottle will not descend below 4ºC but the temperature will fall as it it were affected by a lower temperature.  This is why we are vulnerable to frost bite in low temperatures and high winds.  The heat can be stripped from our skin very rapidly.

The wind chill table demonstrates how quickly the energy can be stripped from
a heat-producing object

Because a building produces heat, it is also affected by the wind chill effect.

This is because heat is stripped away more quickly from an object subjected to wind.

They just can't tell us because, unlike people, they generally have no sensors to register the effect and they do not normally shiver.  It generally relates to the amount of additional heat a building has to produce to compensate for the wind chill effect.

Buildings in exposed locations (top row above) will feel wind chill more than
buildings in sheltered locations or less exposed surface area (bottom row).

Fortunately the wind chill effect is subject to conditions which can be influenced by building design.  This could save up to 20% of energy used for heating.

Adding an additional skin to the building can create a zone 20 to 200cm where air can be
tempered and controlled to reduce the wind chill effect.

Buildings with a single skin or narrow ventilation cavity are more affected by wind chill.  Adding additional layers, obstacles or landscaping can reduce the the affect.

Landscaping and trees can reduce the the exposure of a building to the wind (left)

Adding a secondary skin to the building can create a controlled environmental space reducing wind chill exposure (right)

Building in to the ground, under a green roof or next to water etc. (left)

Or building a mega roof such as Buckminster Fuller's project for Manhattan (right)

Using a green roof and green living wall reduces wind chill (left)
Using an external wall to shield the building also helps (right)

Some of the many ways building design can be articulated to minimise the affects of wind chill.

How Simple Can Architecture Be?

During a design workshop with a school I was asked by a disgruntled sixth-form student

'Why do you architects make out that your work is so complicated?  All buildings have to do is look good, function and last!'

It's true!  Why do architects overthink certain areas of their work more than others, to the detriment of a 'whole-process' strategy of thinking?  Architects need to ensure that their projects:

1. will look good
2. function properly
3. will last

This staring point is simple and makes a useful framework to work from.

How simple can Architecture be?

Developing this with an idea-gram, the simplicity quickly becomes populated with lots of more complicated procedures and areas of work, but bringing them in to the framework of these three points gives them relevance, importance and establishes context.

Some considerations added to this simple framework

This idea-gram was thrown together with ideas considered relevant to this context.  Every Architect will have a different response.  Several of the areas included here extend beyond the standard Architect's scope of work, suggesting greater integration with project management, construction management, logistics and service & maintenance areas for example.   To ensure these three headline criteria are successful,  perhaps architecture does require a greater degree of involvement with other parties engaged in the construction, operation, service and maintenance of a project?

Space Filling Spheres

A small study to see what happens when stacking spheres are converted in to space-filling polyhedra:

It is interesting to play with space-filling shapes in architectural design, just to see what can be created and examine their significance to architecture and design.  Tessellating polyhedra is a big subject.  Part of it are the forms which are created when stacking spheres are converted in to space filling polyhedra.  These are useful because they represent some of the most compact arrangements of forms.  Regularly stacked spheres occupy approximately 74% of space.

In architecture and design, it points to geometric shapes that offer a low surface area to volume ratio, with a potentially low energy loss through the envelope, or components which might prove easier to move and transport.

There are several ways to stack spheres in compact arrangements, but they seem to fall in to two basic arrangements.  Stacking spheres with a square base also creates an arrangement with a triangular base on the diagonal.  Working with a triangular base, the stacking arrangement offers the opportunity to rotate the second layer through 60º.  The spheres still stack but create different arrangements and different space filling polyhedra.

Matching the arrangement of the layers gives a trapezo-rhombic dodecahedron as a space-filling polyhedra.

Trapezo-rhombic dodecahedron

Rotating the arrangement of layers gives a rhombic dodecahedron as a space filling polyhedra.

Rhombic dodecahedron

The trapezo-rhombic dodecahedron and the rhombic dodecahedron are similar.  If a rhombic dodecahedron is sliced across the central horizontal axis and one half mirrored, it creates the trapezo-rhombic dodecahedron.

Trapezo-rhombic dodecahedron to rhombic dodecahedron
slicing through the horizontal plane, making a mirror image and reapplying

It also replicates the arrangement of atoms and crystal structures in nature.

Making the rotation about the horizontal centre of the arrangement creates a cuboctahedron.
Keeping the same arrangement throughout creates a variation on the cuboctahedron.
Because the layer arrangements can be changed, there is an infinate variety of ways space-filling spheres can be stacked.
Reference: The Penguin Dictionary of Curious and Interesting Geometry, David Wells, 1991.
The cuboctahedron is one of the key geometries of Buckminster Fuller's Jitterbug. 

The economic stacking of these space filling polyhedra could inform the assembly of units in buildings.

Polyhedra and Architecture

Space-filling polyhedra have been investigated in architecture, art and science fiction as a conceptual link between nature, technology, society and culture.

Postcards from the Edge (of Laggan Bay)

Filming the Machrie Rebuild

Rebuilding the Machrie Hotel was an exciting experience. We captured the progress with time lapse cameras and site photos. Here’s an edited summary.

The Machrie Hotel

The Machrie Hotel from the 18th green

The Machrie Hotel is a very special destination.  Set on Isle of Islay on the edge of the Laggan Bay with the 18 hole Championship Machrie Links course and miles of pristine SSSI beach, the hotel has opened its doors again following a complete refurbishment.  It now boasts 47 luxury bedrooms including lodges and a duplex suite, restaurant and bar, lounges, spa and even a cinema.

The Islay Suite bedroom

The Vision
The Machrie Golf Links and Hotel share the vision of being the go-to destination for Scottish Island Links Golf.  In tandem with the redevelopment of the hotel, the links course also underwent a full reworking to reinstate it as a Championship course and bring it closer to the original Willie Campbell design of 1891.  On approaching the Machrie, guests meet the 4-star hotel which sets the precedent for the Machrie experience, in this isolated and alluring location.

Golf School

Our Role
DesignBox provided full project management and employer's agent services for the Machrie Hotel.  In addition DesignBox led several exercises including the organisation and connection of utilities (water, electricity, BT & fibre data), asbestos removal, demolition works, preparing accommodation for the site team, the logistical organisation of FF&E and OS&E deliveries and managing meetings.

The Reception Lounge

Key Information & The Team
The hotel was procured under a JCT traditional contract under Scottish Law with Hudson Architects as lead consultant and Morham and Brotchie (Oban) as Quantity Surveyors.  Interior design was provided by Peter Young Design with Lighting Design by Victoria Jerram.  The Structural and Services Engineers came from the Glasgow offices of David Narro Associates and Hulley and Kirkwood respectively. 

Machrie 30-seat cinema

CorraMore Construction from Northern Ireland were appointed as the main contractor for the hotel, accompanied by a number of key subcontractors including EDS(NI) for the services, and JB Interiors for the specialist joinery.

The Stag Lounge

Programme
The development of the Machrie Hotel followed a succession of animated summers.  In the summer of 2013 DesignBox was appointed to help secure consent for a mains water connection, a vital asset which had contributed to the Machrie Hotel's closure in 2011.   Following consent to connect, in the summer of 2014, with the Client and Hudson Architects we established the design team and developed the design.  In the summer of 2016 we started construction with CorraMore and following the installation of FF&E and OS&E, the Machrie Hotel re-opened in the late Summer of 2018.

Machrie Hotel at dusk

Special Mentions
The Machrie Golf Links and Hotel is a truly magical place.  The natural environment is full of colour and vibrant light.  Every five minutes the scenery takes on a completely different feel.  This extraordinary location has been made extra special by some key people:  The Clients and Campbell Gray Hotels for sharing and realising their vision for the Machrie Hotel and Golf Links, David (DJ) Russell, Edinburgh Landscaping and the Machrie Green Keeping Team for creating and maintaining this most incredible golf landscape, the hotel's design and contracting teams for executing the design proposals with precision, care and with good humour, but most of all the Clients for seizing the opportunity and having the conviction to create such a special place to share with everyone.

Machrie Hotel's commercial kitchen