Search found 5 matches

by adrian
Mon Aug 24, 2015 7:22 am
Forum: Stella Forum
Topic: How does Stella4D determine the dual?
Replies: 30
Views: 52709

The centroid, for triangle side length of 1, is ~0.419 (according to Mathematica), but ~0.544 (according to Antiprism). Not sure what I've done differently, I see the difference now, ~0.419 is the centroid of volume and ~0.544 is the centroid of the vertices. It is not too difficult to calculate th...
by adrian
Sun Aug 23, 2015 9:34 pm
Forum: Stella Forum
Topic: How does Stella4D determine the dual?
Replies: 30
Views: 52709

The centroid, for triangle side length of 1, is ~0.419 (according to Mathematica), but ~0.544 (according to Antiprism). Not sure what I've done differently, or am missing. The bottom three vertices are at height 0.0, the second three are at height 0.86..., the centroid will be higher than 0.43... (...
by adrian
Sun Aug 23, 2015 3:29 pm
Forum: Stella Forum
Topic: How does Stella4D determine the dual?
Replies: 30
Views: 52709

Going back to the canonical construction of the solid and its dual, we can readily see that your Chestahedron/ellipsoid construction is a simple stretching of the canonical construction and that symmetries relating to the stretching axis are preserved. In particular, the relative volumes and propor...
by adrian
Fri Aug 21, 2015 6:26 am
Forum: Stella Forum
Topic: How does Stella4D determine the dual?
Replies: 30
Views: 52709

The term "dual" isn't well defined for polyhedra. If the base model has central symmetry and you reciprocate in a sphere with this centre then you will probably get general agreement that the result is the shape of the dual. If the base model also has a midsphere and you reciprocate in this then the...
by adrian
Thu Aug 20, 2015 10:18 am
Forum: Stella Forum
Topic: How does Stella4D determine the dual?
Replies: 30
Views: 52709

The canonical form of the chesterhedron is geometrically self-dual by reciprocation in a sphere. conv_hull Chestahedron-Pts.off | canonical -l 15 | pol_recip -a -c M -n 10000 | antiview http://antiprism.com/misc/tri_antiherm_can_dual.png The chesterhedron itself may be geometrically self-dual by rec...