ICOSAEDRON

, or Icosahedron, one of the five regular bodies or solids, terminated by twenty equilateral and equal triangles. It may be considered as consisting of 20 equal and similar triangular pyramids, whose vertices meet in the centre of a sphere conceived to circumscribe it, and therefore having all their heights and bases equal; therefore the solidity of one of those pyramids multiplied by 20, the number of them, gives the solid content of the Icosaedron.

To form or make the Icosaedron.—Describe upon <*> card paper, or some other such like substance, 20 equilateral triangles, as in the figure at the article Regular Body. Cut it out by the extreme edges, and cut all the other lines half through, then sold the sides up by these edges half cut through, and the solid will be formed.

The linear edge or side of the Icosaedron being A, then will the surface be , and the solidity = .

More generally, put A = the linear edge or side, B the surface, and C the solid content of the Icosaedron, also r the radius of the inscribed, and R the radius of the circumscribing sphere, then we have these general equations, viz,| 1st, . 4th, . See my Mensuration, p. 258, 2d edit.