Join every pair of the 5 vertices and 8 edge midpoints of a square pyramid.
geometry/pyramid.triangles New
New entry, edited from material collected for the archive and not yet in a released version.
Problem
Join every pair of the 5 vertices and 8 edge midpoints of a square
pyramid. How many triangles are formed?
A standard square-based pyramid (apex centralized) has 5 vertexes and
8 sides (not faces). Let each vertex be a point. Let the mid-point of
each side be a point. So you have 13 points. Draw lines connecting
EVERY single pair of points and you get a 3-d array of lines. How many
triangles are thus formed in 3-d space?
-- Koh Kew Soon ("Baboo") <law20065@leonis.nus.sg>
Show solution
Answer: 750 triangles.
(These include triangles with 1, 2 or 3 corner(s) resting on
intersection points which are not any of the original 13 points.)
-- Koh Kew Soon ("Baboo") <law20065@leonis.nus.sg>
[ Editor: the poster's own answer; no derivation or check was found in
the collected postings. ]