Hooked Pair Polar

e₃ points up · unit sphere in gray · hidden edges dashed

Hook strength c₃

c₃

b₃ = √(1 − c₃²)

The triangle is fixed: a₁ = √3⁄2, a₂ = 1⁄2.

Readout

m₀ (triangle floor)
m₃ (pair floor)
lowest ξ₂ on P(D)
reached at
farthest vertices
number of cosine vectors
cosine vectors (normalized)
max ‖x‖
cm(D) = 1 ⁄ max ‖x‖

Show

honest prism T × [−1, 1]

the vectors of D

unit sphere

sphere through the farthest vertex

cosine vectors (normalized farthest vertices)

vertex coordinates

Legend

P(D), front faces shaded the prism of the honest pair farthest vertices from the origin cosine vectors (u, or u₁, u₂, … when several vertices are farthest) lowest value of ξ₂ = ⟨x, e₂⟩