Using entire bike frames connected at the standard bike joints, 2D lattices can be formed.
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Cluster 1: Sommerville – multiple part types
Based on the Sommerville tetrahedron, part systems using multiple compatible types can be created that produce more differentiated complex aggregations.
Continue readingCluster 1: Sommerville system – edge based
Using an aggregation system based on regular Sommerville-tetra cells, bike frame clusters can be connected along edges.
Continue readingCluster 1: bike frames inside Sommerville-Tetrahedrons
Combining the concept of bike frames contained in cells with aggregation systems based on the Sommerville-type interconnected structures can be created.
Continue readingCluster 1: Space Filling (Irregular) Tetrahedra – Sommerville
Alongside Hill’s tetrahedra there are also other irregular tetrahedral cell types to fill space, of which the Sommerville 1 tetrahedron is a very promising one regarding our intentions.
The particularity here is, that the No. 1 tetrahedron consist of two “brackets” of each 2 triangles with two edges the length of the square root of 3 and one edge length of 2, connected at an right angle at their edges of the length 2.
Continue readingCluster 1: Space Filling (Irregular) Tetrahedra – Hill
While it is not possible to fill space with regular tetrahedra, there are – according to WOLFRAM – five known irregular space-filling tetrahedral cells, when mirror cells are excluded.
At first we looked at Hill’s tetrahedra and Izidor Hafner “Definitions of Hill’s Tetrahedra” on the Wolfram Demonstrations Project was very helpful in setting up our Grasshopper definitions.
Cluster 1: Rhombic dodecahedron panels
In an alternative concept for discrete aggregation systems that are based on packed volumes, parts could also be defined as individual faces of a solid.
This idea is studied using the faces of rhombic dodecahedrons that can be arranged as a space-filling tesselation.
Cluster 1: Regular Tetrahedral Cells vs. Cluster Modules
After aggregating regular tetrahedra following different set of rules these tetra-units are replaced by by various bike-frame cluster modules.
Each of these cluster modules is made up of 2-3 bike frames from the scanned set and fitted into a regular tetrahedral container. For this study only copies of one single cluster type are populated throughout the aggregated frameworks replacing the regular tetra-units. This is done assuming that other bike-frames within a certain tolerance range can be used to form the same combinations (possibly with a slightly different clipping at the joint-plate areas). The bigger the inventory of bike frames, the more likely it is to find very similar bike-frames.
Fig.1: Bike Cluster TYPE 12 is used for the first study. Dependening on the bike-frames orientation within one tetrahedral cell informed by the respective connection logic (from left to right: face to face, edge to edge, vertex to vertex) the amount of “empty space” locally within one unit varies immensely.
Continue readingCluster 1: Regular Tetrahedral Cells – Packing and Stacking
In parallel to the bike-frame 3d-scanning and finding of bike-frame cluster modules we are trying to find global systems of how to aggregate these regular tetrahedral cells into large frameworks that form closed loops at different scale levels.
Dependent on the aggregation system, such tetra-units containing the bike-frame clusters are connected at either at their 4 vertices, 4 faces, or 6 edges. Depending on the packing or stacking logic as well as on the bike-frame orientation within the cell, these large aggregations vary immensely in density due to different amounts of “negative space”: empty space globally not filled by tetrahedral cells, and locally – within one cell – not filled by bike frames.
This post covers the global aspects. An overview of – or rather zoom in on – these formations, with various types of bike-frame cluster modules replacing the tetra-units, can be found here.
Structure in Nature is a Strategy for Design
In the course of our investigations into tetrahedral cell packing we came across Peter Pearce‘s book “Structure in Nature is a Strategy for Design” (first published in 1978), in which he meticuously documented his investigations of polygons, which, according to him, form the basic reconfigurable building block for environmental structures that are both, space and energy efficient. It has the potential to become our new bible, at least for a while, as long as we are looking into space filling and cell packing.
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