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Anonymous
Dihedral angle - regular pyramid 01/31/26(Sat)11:20:45 No.16902317

Dihedral angle - regular pyramid Anonymous 01/31/26(Sat)11:20:45 No.16902317 [Reply]▶

File: pyramid.jpg (199.6 KB)

199.6 KB

Can someone explain this rather simple and visual way to find the dihedral angle between two planes in a regular square pyramid ?

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Anonymous
01/31/26(Sat)16:57:00 No.16902589

Anonymous 01/31/26(Sat)16:57:00 No.16902589▶

File: download.gif (5.9 KB)

VectorAngle[Cross[{s, 0, 0}, {s/2, s/2, h}], Cross[{s/2, s/2, h}, {0, s, 0}]] == ArcSec[1 + (h/(s/2))^2]

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Anonymous
01/31/26(Sat)17:05:23 No.16902596

Anonymous 01/31/26(Sat)17:05:23 No.16902596▶

>>16902589
Thanks, can you detail how this method is achieved by the drawing ?

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Anonymous
01/31/26(Sat)22:58:02 No.16902979

Anonymous 01/31/26(Sat)22:58:02 No.16902979▶

>>16902596

A = (0, s, 0)
B = (0, 0, 0)
C = (s, 0, 0)
D = [...]
O = (s/2, s/2, h)

E = C – B = C
F = O – B = O
G = A – B = A

U = E × F
V = F × G

U is normal to plane BCO.
V is normal to plane ABO.

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