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全日制普通高级中学教科书(必修)《数学》第二册(下 B)P.53有这样一道练习:任画一个四面体、六面体,分别数一数它们各有多少条棱,多少条对角线,多少个顶点.《教师教学用书》提供的答案是:四面体有6条棱,无对角线,4个顶点;六面体有12条棱,4条对角线,8个顶点.对四面体,答案是正确的,但对六面体,答案则不够全面,因为五棱锥是六面体,它有10条棱,6个顶点,没有对角线.那么,六面体究竟有多少条对角线?
Full-time General Senior High School Textbook (compulsory) The second volume of Mathematics (under B) P.53 There is a practice of drawing a tetrahedron, hexahedron, counting the number of each of them, how many diagonals Line, how many vertices. “Teachers teaching book” provides the answer is: tetrahedron with six ribs, no diagonal, four vertices; hexahedron has 12 ribs, 4 diagonal, 8 vertices. Body, the answer is correct, but for hexahedron, the answer is not comprehensive enough because the pentagonal pyramid is a hexahedron with 10 edges, 6 vertices, and no diagonal. So how many diagonals does a hexahedron have?