Nan Ma also produced a vZome model for the pyritohedral projection of Gosset’s 1_41 Polytope. Like its icosahedral projection it has 64 distinct 3D ball positions after projection. These are represented in the forthcoming building instructions by red connectors. Due to the projection from 7D to 3D, 668 pairs of crossing blue, green or yellow struts must be dealt with. Only 194 of these intersections can been replaced by false vertices, represented by white connectors. Several reasons cause this rather low ratio:
1) No blue-orbit Zometool struts have been produced with length 1-½φ, -½+½φ, 2-φ, ½ or ½+φ.
No yellow-orbit Zometool struts have been produced with length (3-φ)/5, (-8+6φ)/5, 2-φ, (-1+2φ)/5, (6-2φ)/5, (2+φ)/5, 2 or (2+6φ).
No green-orbit Zometool struts have been produced with length (-4+6φ)/10, (3-φ)/10, (-1+2φ)/10, (3-φ)/5, (-1+φ)/2, (2+φ)/10, (-1+2φ)/5 , (1+3φ)/10 or (2+φ)/5.
2) Zometool only produced green-orbit struts with pentagonal pins. Using these, multiple green struts would have to be put in the same hole.
3) Due to the thickness of the Zometool struts and the diameter of the Zometool balls, some struts and/or connectors interfere, although they are not collinear and do not cross mathematically.
4) Sometimes, a configuration of struts and connectors is correct, but cannot be built sequentially.
A physical model of the pyritohedral projection of the 7-demicube requires some standard Zometool struts: 24 b0's, 120 b1's, 66 b2's, 24 b3's, 120 hb3's, 24 y0's, 12 y1's, 144 y3's, 24 g2's, 24 hg0's, 48 hg1's and 96 hg3's. Nevertheless, it needs a lot of 3D printed supplements to the standard Zometool kit. Most of these are refered to on photo's taken during the actual built:
a) hb1-strut
b) monolithical cross of 2 hg1's
c) monolithical cross of b00 and b1
d) monolithical cross of 2 y-struts with length 2, each with 2 rectangular holes
e) monolithical extended triangle of 3 hg3's, each with a triangular hole, and indentations to avoid interference
f) monolithical cross of 2 hb3's, with a rectangular hole through their intersection
g) b-strut length (1/2+φ) with a triangular hole
h) monolithical cross of 2 hg3's, each with 3 rectangular holes and indentations to avoid interference, and a triangular hole through their intersection …
i) … and with redirected tips
j) hg3 with triangular hole, redirected tip …
k) … and indentations to avoid interference
l) monolithical cross of 2 hg1's
m) monolithical cross of 2 hg3's …
n) …with redirected tips
o) b3 with 2 rectangular holes
p/q) y2 with rectangular hole
r) g3 with rectangular and triangular holes, and redirected tip
s) monolithical cross of 2 g3's each with rectangular hole …
t) … and redirected tip
u) b3 with rectangular hole
