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.

This in combination with the global aggregation logic leads to a range of structures with varying degrees of densities:

Fig. 2: The same boundary volume filled with tetra-units (upper row) which in turn contain the same exact same bike-frame cluster (bottom row) but in its 3 different orientation possibilities (Fig.1).

The face to face aggregation (left column) fits 428 tetrahedra and 1284 bike-frames, the edge to edge (middle) 838 tetrahedra and 2496 bike-frames and the vertex to vertex (right) 1036 tetrahedra and 3108 bike-frames inside that specific boundary volume.

Fig 3: face to face
Fig.4 : edge to edge
Fig. 5: vertex to vertex

As all of these bike cluster types leave 1-3 connection plane vacant (the 3 bike frames serve 3 of the 4 faces or vertices and only 3 of the 6 edges), the resulting frameworks have a lot of open loops. These open ends follow the aggregation logic and could be compensated/bridged by either reorienting the frames within the individual tetra-units or by a second iteration aggregation of single frames to connect in between…

Fig. 6: edge to edge aggregation, isolated single layer(s) (upper row: horizontal, bottom: horizontal and vertical)

Fig. 7: vertex to vertex aggregation, isolated single layer(s) (upper row: horizontal, bottom: horizontal and vertical)

A special type of bike cluster (TYPE 18) serves all 4 vertices and produces a global aggregation with closed loops and therefore a structurally viable framework without any additional modifications:

Fig. 8: edge to edge typology of bike cluster TYPE 18 on the left in omparison with TYPE 12 of the previous aggregations, which does not serve connection vertex 1 (marked with a pink sphere)

Fig. 9: vertex to vertex aggregation with bike cluster TYPE 18, resulting in local and global loops.