This is a construction in vZome of a Hyperboloid of Revolution. It is of the form of one sheet.

16 gon field Hyperboloid

This surface is generated from a hyperbola indicated by grid points, as shown in scenes. In this construction, a hyperbola is defined by a grid which has a series of intervals of the form 1, 1/a, 1/a^2, … where a= √2 The grid is formed by determining the limit of the series, which is found to be 2+√2. In this model, the axes of the grid lines are the diagonals of the x and y axes, shown in green. These axes may be called x’ and y’. Paths of curves are shown by lines connecting grid points. It can be shown that for each indicated curve, all grid points are solutions to equations of the form X’ * Y’ = constant, an alternate definition of hyperbola, with the x’ and y’ axes as asymptotes. The indicated hyperbola is then copied by 16-fold rotational symmetry around the y axis.

Another closely related model can be seen Here