25点

$${「25点」}$$

$${半径\sqrt{3}の円球面上の25点}$$

$${NAn\quad(0,\frac{\sqrt{3}}{2},\frac{3}{2})}$$
$${NBn\quad(\frac{\sqrt{2}}{\sqrt{3}},-\frac{1}{2\sqrt{3}},\frac{3}{2})}$$
$${NCn\quad(\frac{1}{2},-\frac{\sqrt{2}}{2},\frac{3}{2})}$$
$${NDn\quad(-\frac{1}{2},-\frac{\sqrt{2}}{2},\frac{3}{2})}$$
$${NEn\quad(-\frac{\sqrt{2}}{\sqrt{3}},\frac{1}{2\sqrt{3}},\frac{3}{2})}$$

$${AnBn\quad(\frac{\sqrt{2}}{\sqrt{3}},\frac{2}{\sqrt{3}},1)}$$
$${BnCn\quad(\frac{4}{3},-\frac{\sqrt{2}}{3},1)}$$
$${CnDn\quad(0,-\sqrt{2},1)}$$
$${DnEn\quad(-\frac{4}{3},-\frac{\sqrt{2}}{3},1)}$$
$${EnAn\quad(-\frac{\sqrt{2}}{\sqrt{3}},\frac{2}{\sqrt{3}},1)}$$

$${AnAs\quad(0,\sqrt{3},0)}$$
$${BnBs\quad(\frac{2\sqrt{2}}{\sqrt{3}},\frac{1}{\sqrt{3}},0)}$$
$${CnCs\quad(1,-\sqrt{2},0)}$$
$${DnDs\quad(-1,-\sqrt{2},0)}$$
$${EnEs\quad(-\frac{2\sqrt{2}}{\sqrt{3}},\frac{1}{\sqrt{3}},0)}$$

$${AsBs\quad(\frac{\sqrt{2}}{\sqrt{3}},\frac{2}{\sqrt{3}},-1)}$$
$${BsCs\quad(\frac{4}{3},-\frac{\sqrt{2}}{3},-1)}$$
$${CsDs\quad(0,-\sqrt{2},-1)}$$
$${DsEs\quad(-\frac{4}{3},-\frac{\sqrt{2}}{3},-1)}$$
$${EsAs\quad(-\frac{\sqrt{2}}{\sqrt{3}},\frac{2}{\sqrt{3}},-1)}$$

$${SAs\quad(0,\frac{\sqrt{3}}{2},-\frac{3}{2})}$$
$${SBs\quad(\frac{\sqrt{2}}{\sqrt{3}},\frac{1}{2\sqrt{3}},-\frac{3}{2})}$$
$${SCs\quad(\frac{1}{2},-\frac{\sqrt{2}}{2},-\frac{3}{2})}$$
$${SDs\quad(-\frac{1}{2},-\frac{\sqrt{2}}{2},-\frac{3}{2})}$$
$${SEs\quad(-\frac{\sqrt{2}}{\sqrt{3}},\frac{1}{2\sqrt{3}},-\frac{3}{2})}$$

$${X^2+Y^2+Z^2=(\sqrt{3})^2}$$

$${「正25辺体」}$$

$${cf.}$$
$${「12点」}$$