[r-t] Methods as polyhedra
Mark Davies
mark at snowtiger.net
Tue Apr 8 23:44:57 UTC 2008
> Snub cube
Aha! Got this one, too. It's quite tricky, because each vertex has five
edges, hence at least two calls are needed (plus the plain).
The secret to the snub cube is that each vertex takes part in five faces: a
square, and four triangles; but the four triangles are of two different
sorts: three of them share an edge with a square (two with the same square
that our vertex is on, the other one with a neighbouring square), and the
fourth, a "special" triangle, only shares edges with other triangles.
The five edges from each vertex divide up between the square and the four
triangles as follows:
2 edges run along the square, and one each of the "ordinary"
square-sharing triangles.
1 edge runs between two "ordinary" triangles. One of these triangles
shares our square, the other shares a neighbouring square.
2 edges run between the "special" triangle and two ordinary triangles (one
each).
So there is in fact one "special" edge which runs between two "ordinary"
triangles.
So... the squares can form a 4-lead course, call it the plain course. The
"special" triangles can form a 3-lead course, we will call it the single
course. That in fact takes care of all the edges apart from the "special"
edge, the one between two ordinary triangles. This can be a 2-lead bob
course.
Quickly looking for a method and calls to fit this, I find Hordle Place
Doubles, which has a plain-bob type leadhead, 14253. Ring it with a
Grandsire bob (3.1 for 5.1 at the lead end) and you have 13245 for the
special edge. Call a Pink single (3.125 - err, have I got the right name?)
and you get 12534 for the special triangle.
Again, a picture would be nice Hugh, not least to verify I've got it right!
Now... what about an octahemioctahedron?
MBD
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