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Strict orthographic zomeable projections of the 7-demicube (1_41).
In the captions, “balls” means distinct 3D ball positions in the vZome model after projection.
Both 64-ball projections have convex hulls with 30 rhombic faces. The H3 model has the regular rhombic triacontahedron as its hull; the Th model has a pyritohedral 30-face rhombic hull with slim and broad rhombuses.
For the Th- and H3-symmetric models, the strict-orthographic projection matrix is
written up to overall scale as a 7x3 matrix, with one row per 7-demicube
coordinate and columns giving the 3D x,y,z image. These matrices are the raw
sweep matrices scaled by 1/(3phi). The final row is zero, so these projections
are inherited from the corresponding 6-demicube patterns.
1_41_Th_64_balls.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 ],
[ 0, 0, 0 ],
]
1_41_H3_64_balls.vZome:
[
[-phi, -1, 0 ],
[-phi, 1, 0 ],
[-1, 0, -phi ],
[-1, 0, phi ],
[ 0, -phi, -1 ],
[ 0, -phi, 1 ],
[ 0, 0, 0 ],
]