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The name of a 69-sided polygon would be derived from the prefix for 60 when used in the concept of regular polygons (hexacontakai) and the prefix for 9 (ennea), with the suffix -gon at the end of the word. Therefore a 69-sided polygon would be called a hexacontakaienneagon.
Shape names are entirely based on Ancient Greek. The first part dependent on the number of sides/angles/vertices and is simply the equivalent number in Ancient Greek:
1-(h)ena 2-duo 3-tria 4-tetra 5-penta 6-hexa 7-hepta 8-octa 9-(h)ennea 10-deka
The numbers 11 and 12 are compounds of the numbers above:
11-(h)enadeka (1 10), 12 d(u)odeka (2 10)
13-19 are the same but have the Ancient Greek word 'kai' (and) between the two numbers
20 is eikosi but other than that the tens are the numbers above plus -konta
100 is (h)ekaton but the other 100s just as above but using -kosioi instead of -konta
1000 is khilioi with -khilioi as stem
10,000 is murioi with -murioi as stem
To form compund numbers use 'kai' between each number and go smallest to largest or largest to smallest
Shape names are often slightly angelised (ikosi instead of eikosi) and go in order of largest to smallest like English
This is all followed by the Ancient Greek word gon -os - oi (however English does not used declensions so it just becomes -gon)
Therefore a 69 sided shape would be hexakontakaienneagon
Polyamourousagon
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