More examples of Hexagonal spaces

1)

The Edgware Road Music Hall was a masterpiece of planning with segregated circulation systems for stalls and pit and not an inch of wasted space anywhere.

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Kempthorne's 1835 "hexagonal" plan in perspective. - Peter Higginbotham

Kempthorne's hexagonal or "Y-plan"design was essentially a variation of the square plan, with three radiating wings rather than four, and with a hexagonal central hub and perimeter.

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Hexagonal home plans

Wide windows span the front, and a rambling deck wraps around the rear of this linked trio of hexagonal units in this Contemporary home plan. Bright and open gathering spaces fill the central hexagon, while bedrooms and bathrooms are in the right-hand section. The third holds a two-car garage with a workbench and plenty of storage.

from http://www.associateddesigns.com/plan-detail.cfm?id=10016

4)

Hexagonal home plans

This handsome hexagonal home plan is aptly named. It offers panoramic views from all of the rear rooms, plus the wide upper deck and covered lower patio. A double-wide stone chimney vents two fireplaces: a two-sided fireplace on the main floor, and a standard fireplace in the spacious family room below.

from http://www.associateddesigns.com/plan-detail.cfm?id=10249

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Upper Floor Plan

The flat portion of the roof continues around the perimeter of the house and extends into the interior to form soffits. The sloped standing-seam metal roof sits on top of the flat roof and forms clerestories at the gabled ends.

Main Floor Plan

Lower Floor Plan

A large 10 foot high retaining wall was all that remained of the previous home after it burned, and this was incorporated in the design as shown on the lower level plan; it is the only wall not built on the hexagonal pattern.

from http://hickmandesigns.com/8Skyline/Skyline.htm

8)

Hedley Bull Centre for World Politics - Lyons Architects

Melbourne architectural and urban design practice Lyons have completed a new research centre at the Australian National University in Canberra, Australia.

As an object in-the-round, the building marks its prominent street corner. The form is cut through on the principle facade, connecting inside and outside and giving views to the surrounding Canberra hills.

from http://www.dezeen.com/2008/11/30/hedley-bull-centre-for-world-politics-by-lyon-architects/

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OMA in Singapore

"Office for Metropolitan Architecture has announced a large residential complex containing over 1000 apartments in Singapore.

"The project will comprise 32 apartment blocks, each six stories tall, stacked in hexagonal

arrangements. The announcement follows OMA's appointment last year to design a 36-storey residential tower in Singapore."

from http://best-housedesign.blogspot.com/2008_02_01_archive.html

11)

Vertical City Filled with Hexagon houses

Tay Yee Wei, the Malaysian architect publishing a towering vertical city design filled with hexagonal housing units recently. That unique design offer a solution to urban population growth problems in Asian cities.

The tower itself only serves as a scaffolding. As the population of urban areas fluctuates, modular units can be "plugged in or out"to the structure to accommodate an expanding population.

This vertical city Development was inspired by Le Corbusier's theory "a house is a machine for living". This development project essentially rotates a sprawling community into a vertical orientation. The city puts down the initial costs and retains ownership of the primary structure, which is made of reinforced concrete.

from http://www.architecture-view.com/2010/09/22/fascinating-vertical-city-filled-with-hexagonal-housing-units/vertical-city-filled-hexagon-houses/

12)

Bulwark

Doubtful points

What is an efficient space? I decided a room as a regular hexagonal space because the shape of it can make the largest room by the smallest materials. And I thought about interiors. What it should be look like? What is the best way to set the place with furnitures, windows and etc? Should I make those really different from rectangle rooms because of the space is different?

First, I need to start to think about what is the basic factors and what factors have to be in rooms.

Examples of Hexagonal space

1)

Bodiam castle hexagon room

this photograph shows a view from the ground floor that is looking up to the top of the hexagonal rooms.

There were three floors in the south east tower with hexagonal rooms. Each room had a fireplace and a garderobe.

2)

20x20x20 Hexagon Frame/Cable Tents

3)

Moctagon - Scholl Klaus, Gerland Janine

Just turn this house and you'll have another room : From sleeping to writing and lounging. The Moctagon uses the smallest space to offer you all the spaces that you need to feel at home. To close the Moctagon house, you turn the two parts of the house into the sleeping mode. It's like living in a walking wheel. You just step into one corner and then it turns into another room.

4)

Hexagon 3 - Johann Schorr

The Hexagon 3 is a house that is made of a structure of cardboard. Its hexagonal design is flexible and durable together. Also the furniture in this architecture is made out of the card board it is built with.

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Hex Shelf

Moving from place to place a lot, nomads need quick, easy ways to create a personalized space. I prototyped and then fabricated a modular, hexagon shelving system to address this need. Why hexagonal? Turns out that after the circle, the hexagon is the most efficient shape.

from http://www.miksovsky.com/chris/thesis/nomads/hexshelf/hexshelf.htm

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from http://earthbagplans.wordpress.com/2009/05/15/earthbag-pods/

So far ...

So far I looked about which shape would be practical.

If vertices of a regular polygon become more in a circle, the area of a regular polygon would be larger. And it will be getting closer to a circle shape.

But, if we want to fill up a space without spare spaces, make the space as the largest area and less circumference length or materials to use, a practical shape would be a regular hexagon.

So, I decided the space shape as hexagon.

Cyclic Polygons

In geometry, the Japanese theorem states that no matter how one triangulates a cyclic polygon, the sum of inradii of triangles is constant.

sum of the radii of the green circles = sum of the radii of the red circles

Tessellation

A tessellation or tiling of the plane is a pattern of plane figures that fills the plane with no overlaps and no gaps. One may also speak of tessellations of parts of the plane or of other surfaces. Generalizations to higher dimensions are also possible. Tessellations frequently appeared in the art of M. C. Escher.

- Types of hexagon tessellation -

Here's the familiar tessellation of the regular hexagon:

Any hexagon with opposite sides of equal length and opposite angles equal can form a periodic tessellation:

K Reinhardt in his 1918 doctoral thesis Über die Zerlegung der Ebene in Polygone found that there are just three distinct cases of convex hexagons (that is, hexagons with all interior angles less than 180 degrees) that tessellate.

The three cases are:

An example of the first case is illustrated here:

An example of the second case is illustrated here. Note that half the hexagons have been turned over:

The following illustrates an example of the third case:

The hexagon has all side lengths equal and two opposite angles of 90 degrees:

There is a whole family of such radial tessellations (angle 72 degrees and 5 hexagons round the centre point, angle 60 degrees and 6 hexagons round the centre point, and so on..). There are also tessellations with a square or octagon at the centre.

If we consider hexagons which are not convex, a whole range of possible tessellations arise. One interesting shape I've looked at is a chevron, made of 4 equilateral triangles. 6 chevrons can form a hexagon. Also 4 chevrons can form a hexagon. Both of these can themselves tile the plane of course:

- How to make your own Hexagon Tessellation -

Draw a hexagon to use as the basis of your tessellation.

It needn't be a regular hexagon, but make sure that you can draw a line between opposite corners of your hexagon that passes through the centre, and that opposite corners are the same distance from the centre (shown by the solid green line here). This makes sure it will tessellate.

Mark the corners of the hexagon and remove the sides.

Now draw a curve through four of the corners, replacing three sides of your previous hexagon.

Take a copy of one of the sides and paste it exactly onto the opposite side. The corners should line up.

Do the same with the next side.

And finally the last side.

If you found that there was an overlap when you pasted, you'll have to go back and redraw the first curve.

Now decorate your shape

It tessellates like this

If you start with a concave hexagon, and go wild with the curves, you might end up with something like this:

which tessellates, believe it or not