[Woodcarver] Drafting pyramids

[Jean Athey]

Hello folks,
I want to build, then relief-carve, a mantel clock
shaped as a square-based pyramid. If anyone has
experience in drafting the angles/bevels needed to
construct one, I'd appreciate hearing from you. I've
drawn a triangle that I like and which would look good
with my 4" round clockface mounted into it--I started
with a 10 inch baseline; the other two legs of the
triangle (when drafted at a 60 degree angle as
measured from each end of my baseline) meet at a point
about 8-3/4 inches high at the tip. I'm not married to
this dimension, it just looked nice, and gave me a
pleasing size for a mantel clock with a 4" face. 

Problem is, I don't know what angle/baseline length is
needed to form a perfect square pyramid. Think I need
a formula of some kind to know what combination of
baseline/side measurements will meet correctly, so I
can draft pattern sizes that work. Will four 60-degree
triangles form a pyramid when mounted on a square
base? If not, at what angle do I need to cut the legs
in order to make it work? (Egypt's Great Pyramid used
51-degree angles, but when you lay it out, a 51-degree
pyramid is real "squatty"--a 5" base gives you a 3"
high triangle, meaning that for roughly every two
inches in base length you add, you only get 1" of
height. I'd like a "taller" clock, hence the 60+
degree angle.)

You'd think that I could solve this, but no (unless I
just do a bunch of trial and error--there must be a
formula.) Even when I get the side angle issue
answered, there is the problem of board thickness. If
I use 3/4" stock for the pyramid sides, how much do I
need to bevel each side in order to get my angled
joints to fit snugly with no gap? Boy, I need a
"numbers" person--I've spent hours on the web, and
although I've found lots of stats, they don't solve my
specific questions concerning drafting my dimension
angles and bevels.

Anyone want to take a shot at it? 

Jean 
Avila Beach, CA

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