using eulers formula, how many edges does a polyhedron with 20 faces and 12 vertices have?

? edges

eulers formula: $f + v = e + 2$

Question

using eulers formula, how many edges does a polyhedron with 20 faces and 12 vertices have?

?  edges

eulers formula: $f + v = e + 2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Eulers Formula", "Polyhedron Properties" ], "new_concepts": [], "current_concepts": [ "Eulers Formula", "Polyhedron Properties" ] } ## Identify the given values $$ \begin{aligned} F &= 20 \ V &= 12 \end{aligned} $$ ## Apply Euler's formula $$ \begin{aligned} F + V &= E + 2 \ 20 + 12 &= E + 2 \ 32 &= E + 2 \end{aligned} $$ ## Solve for the number of edges $$ \begin{aligned} E &= 32 - 2 \ E &= 30 \end{aligned} $$ Using Euler's formula, how many edges does a polyhedron with 20 faces and 12 vertices have? 30 edges { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Eulers Formula" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given values

Apply Euler's formula

Solve for the number of edges

Answer: