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To be able to tessellate where a vertex meets other vertices, the total of those angles must be a full circle of 360°. The interior angle of an Octagon is 135° which does not divide into 360° which means there cannot be a complete number of vertices meeting and so it cannot, by itself, tessellate.

However, two octagons meeting at a point would have 135° + 135° = 270° leaving 90° which is the interior angle of a square. So octagons and squares together will tessellate.

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Wiki User

9y ago

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More answers

A regular octagon cannot tessellate because the interior angles of an octagon are 135 degrees, which does not evenly divide into 360 degrees, the total angle around a point. In order for a shape to tessellate, the sum of the interior angles must evenly divide into 360 degrees. Since the interior angles of a regular octagon do not meet this criterion, it cannot tessellate without gapping or overlapping.

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ProfBot

5mo ago
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Seeee

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Anonymous

5y ago
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