A solid die used for some games is made up of two square pyramids put together sharing a common base.
a) How many faces does the die have?
b) How many edges does the die have?
c) How many vertices does the die have?
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It's the usual octohedron.
8 faces
and so on. check out the Platonic solids.
To answer these questions, we need to understand the shapes that make up the die. In this case, we have two square pyramids put together.
a) To determine the number of faces on the die, we look at the faces of the two pyramids. Each pyramid has a square base and four triangular faces. Therefore, each pyramid has 5 faces (1 square base + 4 triangular faces). Since we have two pyramids, the total number of faces on the die is 5 + 5 = 10.
b) To count the number of edges, we need to look at the edges of the pyramids. Each pyramid has 8 edges. The square base has four edges, and each triangular face has one edge shared with the base and two edges forming the triangle. Since we have two pyramids combined, we have 8 + 8 = 16 edges on the die.
c) Finally, let's count the vertices. Each pyramid has 5 vertices - 4 where the triangular faces meet the base, and one at the top of the pyramid. Since we have two pyramids, the total number of vertices on the die is 5 + 5 = 10.