having eight angles and eight sides.

1565–75; octagon + -al, replacing earlier octogonal < Neo-Latin octōgōnālis, equivalent to octō- octo- + Greek gōn(ía) angle + -ālis -al1

octagonally, adverb
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World English Dictionary
octagonal (ɒkˈtæɡənəl)
1.  having eight sides and eight angles
2.  of or relating to an octagon

Collins English Dictionary - Complete & Unabridged 10th Edition
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Word Origin & History

1570s, from octagon.
Online Etymology Dictionary, © 2010 Douglas Harper
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American Heritage
Science Dictionary
octagon   (ŏk'tə-gŏn')  Pronunciation Key 
A polygon having eight sides.

octagonal adjective (ŏk-tāg'ə-nəl)
The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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Example sentences
He had returned to the comfort of this glamorous gym carpeted in a
  red-green-and-beige octagonal design.
These novel crayons aren't really round-they are more octagonal, so they don't
  roll away as easily.
It is not a large building but exquisitely beautiful, with a distinctive
  octagonal tower.
The octagonal central chamber contains the cenotaph with diagonal sides leading
  to the corner-chambers.
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