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Strict orthographic zomeable projections of the 6-demicube (1_31, the demihexeract).
In the captions, “balls” means distinct 3D ball positions in the vZome model after projection.
For the Th- and H3-symmetric models, the strict-orthographic projection matrix is
written up to overall scale as a 6x3 matrix, with one row per 6-demicube
coordinate and columns giving the 3D x,y,z image. These matrices are the raw
sweep matrices scaled by 1/(3phi). The emitted .vZome files then apply the
manifest’s physical post-scale so visible edges are practical standard struts.
1_31_Th_32_balls_a.vZome:
[
[-phi, 0, -1/phi ],
[-phi, 0, 1/phi ],
[-1/phi, -phi, 0 ],
[-1/phi, phi, 0 ],
[ 0, -1/phi, -phi ],
[ 0, 1/phi, -phi ],
]
1_31_Th_32_balls_b.vZome:
[
[-phi, 0, -1/phi ],
[-phi, 0, 1/phi ],
[-1/phi, -phi, 0 ],
[-1/phi, phi, 0 ],
[ 0, -1/phi, -phi ],
[ 0, -1/phi, phi ],
]
1_31_H3_32_balls_a.vZome:
[
[-phi, -1, 0 ],
[-phi, 1, 0 ],
[-1, 0, -phi ],
[-1, 0, phi ],
[ 0, -phi, -1 ],
[ 0, phi, -1 ],
]
1_31_H3_32_balls_b.vZome:
[
[-phi, -1, 0 ],
[-phi, 1, 0 ],
[-1, 0, -phi ],
[-1, 0, phi ],
[ 0, -phi, -1 ],
[ 0, -phi, 1 ],
]