最近有学生问笔者这样一个问题:正方体的顶点构成的四面体中,有多少个四面体的四个面都是直角三角形?经过一番思索,笔者才得出答案,是24个.问题解决后,引发了笔者的教学思考,于是便对此问题进行了探究,得出了一系列问题,这些问题的实质是如何对正方体顶点构成的四面体进行分类,下面一一进行探究. Recently, a student asked the author such a question: the vertices of the cube constitute the tetrahedron, the number of tetrahedron four sides are right-angled triangle? After some thought, I came to the answer is 24. After the problem is solved , Triggered the author’s teaching thinking, so he explored the issue, come to a series of questions, the essence of these questions is how to classify the tetrahedron formed by the vertices of the cube, the following one by one to explore.