Euler, a great mathematician, discovered and proved the formula about the relationship between the vertex (V), the number of edges (E) and the number of faces (f) of a polyhedron______ ．

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• 1. If a polyhedron has 12 edges and 6 vertices, then it is a polyhedron______ The surface of the body
• 2. If a polyhedron has 12 edges and 6 vertices, then it is a polyhedron______ The surface of the body
• 3. A polyhedron with 12 vertices and 20 faces. How many edges is this polyhedron As above
• 4. Is there a polyhedron with 10 faces, 30 edges and 20 vertices? (hint: complete according to Euler formula.)
• 5. According to Euler's formula, think about a polyhedron with 10 faces, 30 edges and 20 vertices?
• 6. Fill in the table according to the number of faces, vertices and edges of the polyhedron shown in the figure below. What rules do you find?
• 7. A polyhedron has 20 vertices and 30 edges. It has () faces. This geometry is ()
• 8. Using Euler's formula, think about a polyhedron with 10 faces, 30 edges and 20 vertices
• 9. Proof: if the projection from the vertex of a triangular pyramid to the bottom is the perpendicular center of the bottom triangle, then the projection from any vertex of the bottom triangle to the opposite side must also be the perpendicular center of the triangle
• 10. 49. What condition does a triangular pyramid satisfy that the projection of its vertex on the bottom is the perpendicular of the triangle on the bottom?
• 11. A math problem in junior high school: if each face of a polyhedron is a Pentagon and each vertex has three edges at one end, then the polyhedron has () edges, There are () faces. For mathematical experts to solve, idle people get out of the way, thank you!
• 12. A polyhedron has 12 faces and 30 edges. How many vertices are there?
• 13. If the number of faces of a polyhedron is 8 larger than the number of vertices, and it has 30 edges, then the number of vertices of the polyhedron is
• 14. Read the following materials: in 1750, Euler listed some properties of polyhedron in his letter to Goldbach, one of which is: if V, e and F are used to represent the vertex number, edge number and face number of convex polyhedron, then V-E + F = 2. This discovery is the famous Euler theorem. According to the materials read, we complete: if the face number of a polyhedron is 12 and the edge number is 30, then the vertex number of a polyhedron is 12 The number of points is______ ．
• 15. If the number of faces and edges of a polyhedron is 5 and 8, then the number of vertices is 1_____ .
• 16. If a polyhedron has 6 vertices and 12 edges, its number of faces is () a.6 B.7 c.8 d.9
• 17. What is the surface area of the inscribed sphere of a cube with two edges
• 18. What is the surface area of the inscribed sphere of a cube with side length 2
• 19. A cube with edge length a is inscribed with a sphere whose surface area is
• 20. What is the surface area of the circumscribed sphere of a cube with four edges? 12 π or 24 π, and 32 π, 48 π It's that one