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QuestionMathematics
How many faces, edges, and vertices does a triangular pyramid have?
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Answer
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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Understand the Geometric Shape
A triangular pyramid (also called a tetrahedron) is a three-dimensional geometric solid with triangular faces.
Step 3:: Count the Faces
- Total number of faces: $$4$$ faces
- The base is one triangular face - There are 3 additional triangular faces that connect to the base
Step 4:: Count the Edges
- Total number of edges: $$6$$ edges
- Each triangular face has 3 edges - The base triangle has 3 edges - The edges connecting the base to the apex are 3 more edges
Step 5:: Count the Vertices
- Total number of vertices: $$4$$ vertices
- The base has 3 vertices - There is 1 additional vertex at the apex (top point)
Final Answer
- Faces: 4 - Edges: 6 - Vertices: 4 Note: This follows the classic Euler characteristic for a tetrahedron, which is the simplest possible three-dimensional polyhedron.
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