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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{{1}}{{3}}{}\frac{\sqrt{{3}}}{\sqrt{{-}\frac{{1}}{{3}}{+}\frac{{2}}{{3}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}{/}{3}}{-}\frac{{1}}{{9}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}{/}{3}}{}\sqrt{{11}}{}\sqrt{{3}}{-}\frac{{1}}{{6}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}{/}{3}}{+}\frac{{1}}{{18}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}{/}{3}}{}\sqrt{{11}}{}\sqrt{{3}}}}{,}\frac{\frac{{7}}{{18}}{}\sqrt{{3}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}{/}{3}}{+}\frac{{1}}{{9}}{}\sqrt{{3}}{-}\frac{{1}}{{6}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}{/}{3}}{}\sqrt{{11}}{+}\frac{{5}}{{18}}{}\sqrt{{3}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}{/}{3}}{-}\frac{{1}}{{6}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}{/}{3}}{}\sqrt{{11}}}{\sqrt{{-}\frac{{1}}{{3}}{+}\frac{{2}}{{3}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}{/}{3}}{-}\frac{{1}}{{9}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}{/}{3}}{}\sqrt{{11}}{}\sqrt{{3}}{-}\frac{{1}}{{6}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}{/}{3}}{+}\frac{{1}}{{18}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}{/}{3}}{}\sqrt{{11}}{}\sqrt{{3}}}}{,}\frac{{1}}{{9}}{}\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)}{\sqrt{{-}\frac{{1}}{{3}}{+}\frac{{2}}{{3}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}{/}{3}}{-}\frac{{1}}{{9}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}{/}{3}}{}\sqrt{{11}}{}\sqrt{{3}}{-}\frac{{1}}{{6}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}{/}{3}}{+}\frac{{1}}{{18}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}{/}{3}}{}\sqrt{{11}}{}\sqrt{{3}}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}{/}{3}}}\right]{,}\left[\frac{{1}}{{3}}{}\frac{\sqrt{{3}}}{\sqrt{{-}\frac{{1}}{{3}}{+}\frac{{2}}{{3}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}{/}{3}}{-}\frac{{1}}{{9}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}{/}{3}}{}\sqrt{{11}}{}\sqrt{{3}}{-}\frac{{1}}{{6}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}{/}{3}}{+}\frac{{1}}{{18}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}{/}{3}}{}\sqrt{{11}}{}\sqrt{{3}}}}{,}\frac{{1}}{{9}}{}\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)}{\sqrt{{-}\frac{{1}}{{3}}{+}\frac{{2}}{{3}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}{/}{3}}{-}\frac{{1}}{{9}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}{/}{3}}{}\sqrt{{11}}{}\sqrt{{3}}{-}\frac{{1}}{{6}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}{/}{3}}{+}\frac{{1}}{{18}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}{/}{3}}{}\sqrt{{11}}{}\sqrt{{3}}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}{/}{3}}}{,}\frac{{-}\frac{{7}}{{18}}{}\sqrt{{3}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}{/}{3}}{-}\frac{{1}}{{9}}{}\sqrt{{3}}{+}\frac{{1}}{{6}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}{/}{3}}{}\sqrt{{11}}{-}\frac{{5}}{{18}}{}\sqrt{{3}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}{/}{3}}{+}\frac{{1}}{{6}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}{/}{3}}{}\sqrt{{11}}}{\sqrt{{-}\frac{{1}}{{3}}{+}\frac{{2}}{{3}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}{/}{3}}{-}\frac{{1}}{{9}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}{/}{3}}{}\sqrt{{11}}{}\sqrt{{3}}{-}\frac{{1}}{{6}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}{/}{3}}{+}\frac{{1}}{{18}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}{/}{3}}{}\sqrt{{11}}{}\sqrt{{3}}}}\right]{,}\left[\frac{{1}}{{9}}{}\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)}{\sqrt{{-}\frac{{1}}{{3}}{+}\frac{{2}}{{3}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}{/}{3}}{-}\frac{{1}}{{9}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}{/}{3}}{}\sqrt{{11}}{}\sqrt{{3}}{-}\frac{{1}}{{6}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}{/}{3}}{+}\frac{{1}}{{18}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}{/}{3}}{}\sqrt{{11}}{}\sqrt{{3}}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}{/}{3}}}{,}\frac{{-}\frac{{7}}{{18}}{}\sqrt{{3}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}{/}{3}}{-}\frac{{1}}{{9}}{}\sqrt{{3}}{+}\frac{{1}}{{6}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}{/}{3}}{}\sqrt{{11}}{-}\frac{{5}}{{18}}{}\sqrt{{3}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}{/}{3}}{+}\frac{{1}}{{6}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}{/}{3}}{}\sqrt{{11}}}{\sqrt{{-}\frac{{1}}{{3}}{+}\frac{{2}}{{3}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}{/}{3}}{-}\frac{{1}}{{9}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}{/}{3}}{}\sqrt{{11}}{}\sqrt{{3}}{-}\frac{{1}}{{6}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}{/}{3}}{+}\frac{{1}}{{18}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}{/}{3}}{}\sqrt{{11}}{}\sqrt{{3}}}}{,}\frac{{1}}{{3}}{}\frac{\sqrt{{3}}}{\sqrt{{-}\frac{{1}}{{3}}{+}\frac{{2}}{{3}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}{/}{3}}{-}\frac{{1}}{{9}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{2}{/}{3}}{}\sqrt{{11}}{}\sqrt{{3}}{-}\frac{{1}}{{6}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}{/}{3}}{+}\frac{{1}}{{18}}{}{\left({17}{+}{3}{}\sqrt{{11}}{}\sqrt{{3}}\right)}^{{1}{/}{3}}{}\sqrt{{11}}{}\sqrt{{3}}}}\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.

 See Also

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