勾股4态

共球点

点坐标符号

分坐标x

分坐标y

分坐标z

垂心重心共球半径

点

8

O

$\frac{1}{2}\left(a+bct\frac{v+2abc}{v}\right)$

$\frac{1}{2}\left(b+act\frac{v+2abc}{v}\right)$

$\frac{1}{2}\left(c+abt\frac{v+2abc}{v}\right)$

$r_O^2=4R_G^2-r_H^2$

线

20

$O_{1/2}=G$

$\frac{1}{4}\left(a+bct\right)$

$\frac{1}{4}\left(b+act\right)$

$\frac{1}{4}\left(c+abt\right)$

$r_{O/2}^2=R_G^2=\frac{a^2+b^2+c^2+d^2}{16}$

面

12

$O_{1/3}$

$\frac{1}{6}\left(a+bct\frac{v-2abc}{v}\right)$

$\frac{1}{6}\left(b+act\frac{v-2abc}{v}\right)$

$\frac{1}{6}\left(c+abt\frac{v-2abc}{v}\right)$

$r_{O/3}^2=\frac{1}{3^2}\left(4R_G^2-r_H^2\right)$

体

6

$O_{1/4}$

$\frac{1}{8}\left(a+bct\frac{v-4abc}{v}\right)$

$\frac{1}{8}\left(b+act\frac{v-4abc}{v}\right)$

$\frac{1}{8}\left(c+abt\frac{v-4abc}{v}\right)$

$r_{O/4}^2=\frac{1}{4}\left(R_G^2-r_H^2\right)$

4

H

$\frac{-a{b}^2{c}^{2}t}{v}$

$\frac{-a^{2}b{c}^{2}t}{v}$

$r_H^2=\frac{a^2{b}^2{c}^2{d}^2}{v^2}$