After the 8 vertices of a cube are cut off, a new geometry is obtained, which has a number of advantages______ Two noodles______ Two vertices______ The edge of the bar

After the 8 vertices of a cube are cut off, a new geometry is obtained, which has a number of advantages______ Two noodles______ Two vertices______ The edge of the bar

If a vertex is cut off, there will be one more face, two more vertices and three more edges. Then the new geometry should have 6 + 8 = 14 faces, 8 + 8 × 2 = 24 vertices and 12 + 8 × 3 = 36 edges

A solid figure has 8 vertices and 6 faces, and each vertex has the same number of edges. How many edges does each vertex have?

Let every vertex have n edges,
There are 8N / 2 = 4N edges
Using Euler formula of polyhedron
Number of faces + number of vertices - number of edges = 2
∴ 6+8-4n=2
∴ 4n=12
∴ n=3
That is, each vertex has three edges

How many faces does a prism have? How many vertices? How many edges? Guess the case of a seven prism and try to verify your guess

What is n
Face = n + 2 (n facades plus 2 bottom faces)
Vertex = n × 2 (two ground vertices)
Edge = n × 3 (two bottom edges plus inner edges, three times the number of edges)
So the pentagonal cylinder is 5 + 2 = 7, vertex 10, edge 15
Hexagonal prism 8 16 18
Heptagonal 9 14 21