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In homothety, each point P of the set S of all points of unextended space is carried into the point P1 of S collinear with P and a fixed point O of space, and such that $\frac{\mathrm{OP1}}{\mathrm{OP}}=k$, where k is a nonzero real number. Note that OP1, OP denote the sensed magnitudes of OP1 and OP.

For a detailed description of the object created Q, use the routine detail (i.e., detail(Q))

The command with(geom3d,homothety) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{geom3d}\right)\:$

$\mathrm{icosahedron}\left(\mathrm{p1}\,\mathrm{point}\left(o\,0\,0\,0\right)\,1\right)$

$\mathrm{p1}$

$\mathrm{stellate}\left(\mathrm{p2}\,\mathrm{p1}\,10\right)$

$\mathrm{p2}$

$\mathrm{homothety}\left(\mathrm{p3}\,\mathrm{p2}\,3\,o\right)$

$\mathrm{p3}$

$\mathrm{draw}\left(\left[\mathrm{p2}\,\mathrm{p3}\right]\,\mathrm{scaling}=\mathrm{constrained}\,\mathrm{style}=\mathrm{patch}\,\mathrm{lightmodel}=\mathrm{light4}\,\mathrm{orientation}=\left[0\,32\right]\,\mathrm{title}=\mathrm{`homothety\; of\; a\; stellated\; icosahedron`}\right)$