ARCHIMEDE INSTITUTE


Showing posts with label Rhombic Dodecahedral Geometry. Show all posts
Showing posts with label Rhombic Dodecahedral Geometry. Show all posts

ARCHIMEDE NO-WASTE APPROACH

From the start we chose the rhomboid geometry that is made up of identical parallelograms. Just like with squares and rectangles, parallelograms can be made up of rectangular sheathing without wasting any of it.
Here is a demonstration: typically, our standard roof panels can be made up of two 4x8 sheets with no waste, one being cut diagonally , as shown in diagram below. This represent the roof of one 180 ft2 hexagonal module.



This stronger 'vaulted' surface is made up of three planes, each one made up of of-the-shelf building materials. You need to love that since it also applies to walls and underside panels (in the case of stilt houses )

The Rhombic Dodecahedral Geometry


(text from Wikipedia)
The rhombic dodecahedra honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space. It is the Voronoi diagram of the face-centered cubic sphere-packing, which is believed to be the densest possible packing of equal spheres in ordinary space (see Kepler conjecture).

It consists of copies of a single cell, the rhombic dodecahedron. All faces are rhombs, with diagonals in the ratio 1:√2. Three cells meet at each edge. The honeycomb is thus cell-transitive, face-transitive and edge-transitive; but it is not vertex-transitive, as it has two kinds of vertex. The vertices with the obtuse rhombic face angles have 4 cells. The vertices with the acute rhombic face angles have 6 cells.

The rhombic dodecahedron can be twisted on one of its hexagonal cross-sections to form a trapezo-rhombic dodecahedron, which is the cell of a somewhat similar tessellation, the Voronoi diagram of hexagonal close-packing.

In plain English: If you took a can of peas, drained it and packed some of the peas tightly between your two cupped hands, you would obtain:




  • a bunch of peas each with twelve identical flat faces, parallellogram shaped
  • no void between each peas until you separate them
  • very messy hands.
  • The resulting shape is the strongest thing next to a sphere
  • It is arguably the strongest object you can create using flat surfaces



Hundred of houses built this way have been trhough terrible hurricanes and earthquakes,

SOLID GEOMETRICAL CHOICES FOR STRENGTH

This acrylic scale model built in 1979 was the inspiration for a 30 year effort in building stronger better prefabricated homes. The configuration variety provided by these identical panels, their angles of intersection providing 3 axis of resistance to lateral forces instead of 2, the multiple orientations of the views provided gave Poirier a rush he could not resist to build them for all these years. Since 1979, a few changes were brought about, the actual rhombic dodecahedron was actually squashed vertically, then some roofs were transformed into 6-side pyramids, but the essential merit of the shape remained intact as the panels and the shells were proven to be equal or more resistive than planned.
This merit is firstly the unusually high resistance to side loads. This diagram makes it easy to understand what makes this possible. Whatever the direction

HIGHER DENSITY GROUPINGS

The Domus system can me maximized for higher densities quite easily. It's remarquable soundproofing allows for such economy of land and resources.