clustering of an inventory

Applying a clustering algorithm to an inventory of irregular unique objects can help to reduce the complexity involved in designing with such parts significantly. By dividing the inventory items into groups with similar characteristics, each group can then be represented by one “proto-part” instead, therefore reducing the amount of unique elements to be handled in setting up aggregation logics and the aggregation processes.
The decision about the number of different groups (Fig. 1) can be completely left to an algorithm (depending on various predefined – by the programmer – conditions) or be manually determined by the user/designer.

Fig. 1: clustering of inventory with different amounts of groups (“proto-parts”)
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Cluster 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.

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Cluster 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.

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