High, the surface divided into numerous furrows like the ribs of a melon, with projecting angles, which are set with a regular series of stellated spines - each bundle consisting of about five larger spines, accompanied by smaller but sharp bristles - and the tip of the plant being surmounted by a cylindrical crown 3 to 5 in.
The "small stellated dodecahedron," the "great dodecahedron" and the "great stellated dodecahedron" are Kepler-Poinsot solids; and the "truncated" and "snub dodecahedra" are Archimedean solids (see Polyhedron).
Four such solids exist: (I) small stellated dodecahedron; (2) great dodecahedron; (3) great stellated dodecahedron; (4) great icosahedron.
The small stellated dodecahedron is formed by stellating the Platonic dodecahedron (by "stellating " is meant developing the faces contiguous to a specified base so as to form a regular pyramid).
The great stellated dodecahedron is formed by stellating the faces of a great dodecahedron.
The great icosahedron is the reciprocal of the great stellated dodecahedron.
Poinsot gave the formula E 2k = eV + F, in which k is the number of times the projections of the faces from the centre on to the surface of the circumscribing sphere make up the spherical surface, the area of a stellated face being reckoned once, and e is the ratio " angles at a vertex /21r" as projected on the sphere, E, V, F being the same as before.
Cayley gave the formula E + 2D = eV + e'F, where e, E, V, F are the same as before, D is the same as Poinsot's k with the distinction that the area of a stellated face is reckoned as the sum of the triangles having their vertices at the centre of the face and standing on the sides, and e' is the ratio: " the angles subtended at the centre of a face by its sides /2rr."
It is self-reciprocal; the cube and octahedron, the dodecahedron and icosahedron, the small stellated dodecahedron and great dodecahedron, and the great stellated dodecahedron and great icosahedron are examples of reciprocals.