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decahedron(height:in:restitution:)

Creates a decahedron, a symmetrical, ten-faced polyhedron with kite-shaped faces, that the player tosses during gameplay.

Declaration

static func decahedron(height: Float, in unit: UnitLength = .meters, restitution: Float? = nil) -> TossableRepresentation

Parameters

  • height:

    The height of the decahedron.

  • unit:

    The unit of measurement for the height.

  • restitution:

    The coefficient of restitution, in the range [0, 1].

Discussion

The vertices for the simulated pentagonal trapezohedron (or deltohedron) are oriented with one face toward +y and the top spindle vertex of the top face toward -z. A pentagonal trapezohedron has 10 identical symmetric kite shaped faces arranged around a spindle axis. In the physics simulation, it is scaled along the spindle axis to place all vertices exactly on the surface of a circumscribed sphere. In this orientation, the height (h) is measured from face to opposing face, and the vertices have the following coordinates, which all lie on a circumscribed sphere of radius r = 5^(1/4) · h/2 = sqrt(2·phi - 1) · h/2 with an axial tilt angle ⍬ with tan(⍬) = sqrt(2/phi): ±Y face: ±{ 0, +1, -sqrt(2/phi) } · h/2, Equator: ±{ 0, -1, -sqrt(2/phi) } · h/2, ±{+sqrt(2), -1/phi^3, -sqrt(2/phi) / phi^2 } · h/2, ±{+sqrt(2)/phi, +1, +sqrt(2/phi) / phi } · h/2, ±{-sqrt(2)/phi, +1, +sqrt(2/phi) / phi } · h/2, ±{-sqrt(2), -1/phi^3, -sqrt(2/phi) / phi^2 } · h/2

Higher restitution values indicate materials that conserve kinetic energy during collisions, causing objects to bounce off each other elastically. Lower values suggest materials that absorb kinetic energy, resulting in less bounce and more energy loss upon impact.

See Also

Creating geometric shapes