According to Euler's formula, think about a polyhedron with 10 faces, 30 edges and 20 vertices?

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• 1. 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?
• 2. A polyhedron has 20 vertices and 30 edges. It has () faces. This geometry is ()
• 3. Using Euler's formula, think about a polyhedron with 10 faces, 30 edges and 20 vertices
• 4. 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
• 5. 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?
• 6. In a triangular pyramid a-bcd, the projection of D in plane ABC is e, and the projection of a in plane BCD is f (1) If de intersects AF, verify that ad is perpendicular to BC (2) Is the inverse proposition of (1) Tenable
• 7. In the triangular pyramid abc-a1b1c1, AB is perpendicular to AC, the projection of vertex A1 on the bottom ABC is exactly point B, and ab = AC = A1B = 2 Find the angle between Aa1 and ABC (2) Determine a point P on edge b1c1 so that AP = 14 under the root sign, and calculate the cosine value of dihedral angle p-ab-a1 Answer 2 under the root sign 5 / 5 Newspapers 20-5
• 8. What is the volume of a square with a volume of 8 if its vertices are on the sphere?
• 9. The ratio of the volume of a cylinder to the volume of a sphere is 3:2. Then the ratio of the side area of the cylinder to the surface area of the sphere is () A. 1：1B. 1：2C. 2：3D. 3：2
• 10. If the vertices of a square whose edge length is 2cm are all on a sphere, then the volume of the sphere is
• 11. Is there a polyhedron with 10 faces, 30 edges and 20 vertices? (hint: complete according to Euler formula.)
• 12. A polyhedron with 12 vertices and 20 faces. How many edges is this polyhedron As above
• 13. If a polyhedron has 12 edges and 6 vertices, then it is a polyhedron______ The surface of the body
• 14. If a polyhedron has 12 edges and 6 vertices, then it is a polyhedron______ The surface of the body
• 15. 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______ ．
• 16. 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!
• 17. A polyhedron has 12 faces and 30 edges. How many vertices are there?
• 18. 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
• 19. 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______ ．
• 20. If the number of faces and edges of a polyhedron is 5 and 8, then the number of vertices is 1_____ .