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April 8th, 2017, 01:05 AM   #1
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Off-Centre Sphere Stacking. Trigonometry

Dear My Math Forum,

I have been trying to figure out how to find the position(height) of spheres on a 2nd layer above a 1st layer of HCP Spheres. The 2nd layer are offset from the 'deep hole' of the 1st layers 3 spheres. They do not sit in the centre.

I have attached an image to show the positions. I want to work out the 'white x' height of the 2nd layer

If I place a sphere at 0,0,0 (centred in the image) the 'x' or 'y' positions of the layer 1 spheres are
'y' = -.5,
'x' = 0.866 025 403 784 438 646 763 723 170 752 936 183 471 402 63,
'z' = 0

Doubling this number gives me the further sphere positions of layer 1.

Layer 2's spheres are positioned by swopping the 'x' and 'y', still using the 0.866025 number.

What is the height of the 2nd layer. The Spheres are '1' diameter
Attached Images
File Type: jpg off centre stacking.jpg (27.8 KB, 0 views)
File Type: jpg layer 1-2 overlapped.jpg (48.1 KB, 0 views)
File Type: jpg hcp layer 2.jpg (33.1 KB, 0 views)

Last edited by Slaterdom; April 8th, 2017 at 01:11 AM.
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