【摘要】 垂心四面体中四条高的垂足,四个面的重心及从各顶点与四面体的垂心连线的三等分点,共十二个点共球.试图把垂心改为四面体内的任意点,相应地把四条高线改换为过该点与每个顶点连线的共点直线组时,则将把垂心四面体的十二点球有趣地推广为四面体的十二点二次曲面.更多还原

【Abstract】 The four feet of four altitudes for an orthocenter tetrahedron,the centers of gravity of the four faces,the trisection of the line segments from the orthocenter to four summits,total twelve points lie on same sphere,which is known as twelve-point sphere. If the orthocenter can be changed into any point within a tetrahedron in this paper,and corresponding the four perpendiculars also can be changed into the four lines segment passing through the given point to the summits of the tetrahedron,the twelve-point sphere can be changed into twelve-point quadric surface.Twelve point sphere of an orthocenter tetrahedron can be generalized to the twelve-point quadratic surface of a tetrahedron.更多还原