Is 3.10.16 a possible vertex type for a vertex surrounded by regular polygons?

Name: Is 3.10.16 a possible vertex type for a vertex surrounded by regular polygons?
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Question

Quizplus · Accepted Answer

A vertex surrounded by regular polygons must satisfy the equation 1/a + 1/b + 1/c > 1/2, where a, b, and c are the numbers of sides of the polygons meeting at the vertex. For 3.10.16, the equation is 1/3 + 1/10 + 1/16 = 0.48125, which is less than 1/2, thus it cannot form a vertex surrounded by regular polygons.

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