incident - Maple Help

geom3d

 incident
 return the vertices incident to a given vertex of a polyhedron

 Calling Sequence incident(ngon, i)

Parameters

 ngon - polyhedron i - positive integer

Description

 • The routine incident returns a list of vertices incident to the i-th vertex of the given polyhedron ngon.

Examples

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

Define a snub cube with center (0,0,0), radius of the in-sphere 1

 > $\mathrm{SnubCube}\left(s,\mathrm{point}\left(o,0,0,0\right),1\right)$
 ${s}$ (1)
 > $\mathrm{nops}\left(\mathrm{vertices}\left(s\right)\right)$
 ${24}$ (2)

Find the coordinates of vertices which are incident to the second vertex

 > $\mathrm{inc}≔\mathrm{incident}\left(s,2\right)$
 ${\mathrm{inc}}{≔}\left[\left[\frac{\sqrt{{3}}}{{3}{}\sqrt{{-}\frac{{1}}{{3}}{+}\frac{{2}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}}{{3}}}}{{3}}{-}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}}{{3}}}{}\sqrt{{11}}{}\sqrt{{3}}}{{9}}{-}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}}{{6}}{+}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}{}\sqrt{{11}}{}\sqrt{{3}}}{{18}}}}{,}\frac{\frac{{7}{}\sqrt{{3}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}}{{18}}{+}\frac{\sqrt{{3}}}{{9}}{-}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}}{{3}}}{}\sqrt{{11}}}{{6}}{+}\frac{{5}{}\sqrt{{3}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}}{{3}}}}{{18}}{-}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}{}\sqrt{{11}}}{{6}}}{\sqrt{{-}\frac{{1}}{{3}}{+}\frac{{2}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}}{{3}}}}{{3}}{-}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}}{{3}}}{}\sqrt{{11}}{}\sqrt{{3}}}{{9}}{-}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}}{{6}}{+}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}{}\sqrt{{11}}{}\sqrt{{3}}}{{18}}}}{,}\frac{\sqrt{{3}}{}\left({\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}}{{3}}}{-}{2}{-}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}\right)}{{9}{}\sqrt{{-}\frac{{1}}{{3}}{+}\frac{{2}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}}{{3}}}}{{3}}{-}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}}{{3}}}{}\sqrt{{11}}{}\sqrt{{3}}}{{9}}{-}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}}{{6}}{+}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}{}\sqrt{{11}}{}\sqrt{{3}}}{{18}}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}}\right]{,}\left[\frac{\sqrt{{3}}}{{3}{}\sqrt{{-}\frac{{1}}{{3}}{+}\frac{{2}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}}{{3}}}}{{3}}{-}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}}{{3}}}{}\sqrt{{11}}{}\sqrt{{3}}}{{9}}{-}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}}{{6}}{+}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}{}\sqrt{{11}}{}\sqrt{{3}}}{{18}}}}{,}\frac{\sqrt{{3}}{}\left({\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}}{{3}}}{-}{2}{-}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}\right)}{{9}{}\sqrt{{-}\frac{{1}}{{3}}{+}\frac{{2}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}}{{3}}}}{{3}}{-}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}}{{3}}}{}\sqrt{{11}}{}\sqrt{{3}}}{{9}}{-}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}}{{6}}{+}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}{}\sqrt{{11}}{}\sqrt{{3}}}{{18}}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}}{,}\frac{{-}\frac{{7}{}\sqrt{{3}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}}{{18}}{-}\frac{\sqrt{{3}}}{{9}}{+}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}}{{3}}}{}\sqrt{{11}}}{{6}}{-}\frac{{5}{}\sqrt{{3}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}}{{3}}}}{{18}}{+}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}{}\sqrt{{11}}}{{6}}}{\sqrt{{-}\frac{{1}}{{3}}{+}\frac{{2}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}}{{3}}}}{{3}}{-}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}}{{3}}}{}\sqrt{{11}}{}\sqrt{{3}}}{{9}}{-}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}}{{6}}{+}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}{}\sqrt{{11}}{}\sqrt{{3}}}{{18}}}}\right]{,}\left[\frac{\sqrt{{3}}{}\left({\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}}{{3}}}{-}{2}{-}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}\right)}{{9}{}\sqrt{{-}\frac{{1}}{{3}}{+}\frac{{2}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}}{{3}}}}{{3}}{-}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}}{{3}}}{}\sqrt{{11}}{}\sqrt{{3}}}{{9}}{-}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}}{{6}}{+}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}{}\sqrt{{11}}{}\sqrt{{3}}}{{18}}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}}{,}\frac{{-}\frac{{7}{}\sqrt{{3}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}}{{18}}{-}\frac{\sqrt{{3}}}{{9}}{+}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}}{{3}}}{}\sqrt{{11}}}{{6}}{-}\frac{{5}{}\sqrt{{3}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}}{{3}}}}{{18}}{+}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}{}\sqrt{{11}}}{{6}}}{\sqrt{{-}\frac{{1}}{{3}}{+}\frac{{2}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}}{{3}}}}{{3}}{-}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}}{{3}}}{}\sqrt{{11}}{}\sqrt{{3}}}{{9}}{-}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}}{{6}}{+}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}{}\sqrt{{11}}{}\sqrt{{3}}}{{18}}}}{,}\frac{\sqrt{{3}}}{{3}{}\sqrt{{-}\frac{{1}}{{3}}{+}\frac{{2}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}}{{3}}}}{{3}}{-}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}}{{3}}}{}\sqrt{{11}}{}\sqrt{{3}}}{{9}}{-}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}}{{6}}{+}\frac{{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}}{{3}}}{}\sqrt{{11}}{}\sqrt{{3}}}{{18}}}}\right]\right]$ (3)
 > $\mathrm{nops}\left(\mathrm{inc}\right)$
 ${3}$ (4)

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