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As per [dic.yahoo.co.jp](http://dic.yahoo.co.jp/) the following four geometric
figures seem to be read as (ateji / gairaigo)
[十角形](http://dic.search.yahoo.co.jp/search?ei=UTF-8&p=%E5%8D%81%E8%A7%92%E5%BD%A2&stype=full&fr=dic)、[九角形](http://dic.search.yahoo.co.jp//search;_ylt=A2Riol2N7odY2EQA7g9Umfd7?p=%E4%B9%9D%E8%A7%92%E5%BD%A2&stype=full&aq=-1&oq=&ei=UTF-8)、[七角形](http://dic.search.yahoo.co.jp//search;_ylt=A2RCK_EF74dY63kAPQlUmfd7?p=%E4%B8%83%E8%A7%92%E5%BD%A2&stype=full&aq=-1&oq=&ei=UTF-8)、[十二角形](http://dic.search.yahoo.co.jp//search;_ylt=A2RimV87.odYnRcANiBUmfd7?p=%E5%8D%81%E4%BA%8C%E8%A7%92%E5%BD%A2&stype=full&aq=-1&oq=&ei=UTF-8)
( _decagon_ , _nonagon_ , _heptagon_ , _dodecagon_ ). As per the same
dictionary, all the other sided figures that have less than 12 sides,
((triangle ---> 6-sides) + octagon + 11-sides), are read using each kanji's
standard 音読み。

So, are these readings ok?

**七角形{ヘプタゴン}**

八角形{はっかくけい} <--- for some reason, normal 音読み reading.

**九角形{ノナゴン}**

**十角形{デカゴン}**

十一角形{じゅういちかくけい} <--- for some reason, normal 音読み reading.

**十二角形{ドデカゴン}**

Are those less commonly known English names (the only one an _English_ native
speaker might know is "decagon") for geometric shapes burrowing their way into
the Japanese language as "ateji / gairaigo"? _Or_ , is it that I'm not
understanding the *dic.yahoo.co.jp" dictionary, and "〜角形" is a straight-up
normal counter that is read with standard 音読み？
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loanwords counters ateji
Could 十角形、九角形、七角形 be read as デカゴン、ノナゴン、ヘパタゴン？
No, those `-ゴン` words are basically rare loanwords and they're not used in
ordinary math classes. (Of course ペンタゴン is famous as the name of a building.)
The dictionary entries you linked just say that the katakana word ヘキサゴン
**means** 六角形, etc. They do not say that 六角形 is read as ヘキサゴン, etc. 七角形 does
not seem to be in the same dictionary, but it's simply because the rule is
fairly simple and the meaning of 七角形 is too obvious to Japanese readers.

  * 三角形: さんかくけい
  * 四角形: しかくけい
  * 五角形: ごかくけい
  * 六角形: ろっかくけい
  * 七角形: しちかくけい / ななかくけい
  * 十二角形: じゅうにかくけい

... and so forth.

かくけい can be replaced with かっけい.
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answer
Not to confuse the issue (hopefully), but it bears noting that any Japanese
word could be given just about any reading -- that's what furigana are for.

Interesting examples I've run across include:

  * 騎士, usually read as きし{kishi}, with the furigana ナイト{naito} instead to match the English word "knight".  
(Though I suppose, to match Monty Python, perhaps クニギット{kunigitto} would be
more fitting. :) )

  * 本気, usually read as [ほんき]{honki}, with the furigana マジ{maji} instead to convey an alternate meaning.
  * 玄人, usually read as くろうと{kurōto}, with the furigana プロ{puro} instead to match the English word "pro".

Manga are chock full of numerous examples of furigana used to apply different
readings to words. Furigana are a wonderful feature of Japanese writing,
providing authors with a means to give any word additional layers of meaning.

That said, in a more specific reply to your question "are these readings ok,"
there are standard readings of Japanese words, and readings that only come
from furigana. Furigana for any given term _might_ be providing the standard
reading. However, if you see a kanji term with katakana furigana, chances are
high that the furigana reading in these cases is non-standard, and only
specific to the text containing this reading.
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