Let the diameter AB of the given sphere be set out, and let it be cut at C so that AC is quadruple of CB,
let the semicircle ADB be described on AB,
let the straight line CD be drawn from C at right angles to AB, and let DB be joined;
let the circle EFGHK be set out and let its radius be equal to DB,
let the equilateral and equiangular pentagon EFGHK be inscribed in the circle EFGHK,
let the circumferences EF, FG, GH, HK, KE be bisected at the points L, M, N, O, P, and let LM, MN, NO, OP, PL, EP be joined.
Therefore the pentagon LMNOP is also equilateral, and the straight line EP belongs to a decagon.
Now from the points E, F, G, H, K let the straight lines EQ, FR, GS, HT, KU be set up at right angles to the plane of the circle, and let them be equal to the radius of the circle EFGHK, let QR, RS, ST, TU, UQ, QL, LR, RM, MS, SN, NT, TO, OU, UP, PQ be joined.