Hacker News Reader

I didn't really get it at first, in fact, I might still not be getting it, but if you draw a line from A to C, then you can see that the triangle ABC will not be similar to DEF... when it should be? I don't know.

View on HN

The triangles don't have to be similar to make it a real pyramid. They only have to be similar of you want the truncation to be made parallel to the base.

For it to be a real pyramid, you only need the side edges lines to meet at the apex, which always happen when the top and bottom triangles are similar.

Similar triangles are a sufficient, but not necessary condition.

The issue is about which edges are in the same plane as which other edges. If this is a polyhedron, AD and BE must be coplanar, and BE and CF must be coplanar. Extending the edges into lines, they don't form a 3-way intersection. G gets projected to the same screen point as some point on line AD, but the only way G can be on line AD is if AD and FC are coplanar. If all three of AD, BE, and FC are coplanar, the entire figure is a flat pentagon (and DE, BE, and FE are not edges).

If G isn't on line AD, then BE and CF can't be a side of the same truncated pyramid.

Reply on news.ycombinator.com