Generalized Waterman Polyhedron from polyhedral packs

the general series are defined as -
The convex hull of the intersection of a closed ball with the lattice(s) of a space filler grouping swept from symmetrically biased locations; polyhedral center, edge mid-point, vertex or face center.
A Generalized Waterman polyhedron, includes any related lattice structuring, wherein pertinent all space fillers become employed to establish a common/combined lattice point set. This Generalized approach is currently able to be manifested and viewed by Antiprism...written by Adrian Rossiter

over 60 different unlimited series of Waterman polyhedron

Generalized Waterman polyhedron derived from integer based grids.

click left hand side below to see related Waterman polyhedron; 1-32, 36 and 48

click image and drag to rotate image

cluster Oh Oh C2v C2v
Oh C4v C3v
fcc Oh Oh C2v Oh
C4v C2v C4v
hcp Oh Oh C2v Oh
C4v C2v C4v
truncated octahedron Oh C4v C2v C3v
Oh C4v Oh C4v
C4v Oh
rhombic dodecahedron
sc and sc offset combined  
truncated tet tet C2v C3v C4v C4v
C2v C4v C4v C4v
with sturts of length square root of 2
truncated tet truncated octahedron cuboctahedron C2v C3v C4v C4v

39coordinate points used for sweep analysis

red points extend from 0,0,0 to 2,2,2 - each block is therefore a length of 2

39 tested Origins

Antiprism itself is a collection of programs that facilitates numerous techniques, like weaves and conversion and merging abilities as well as a viewer. It is also free as well as being extremely versatile.
Here is a additional MASTER page for SPHERE packed ccp applets - links - software related - examples - write ups - etc

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