"That English dictionary is not thick at all."
The following is an answer from Japanese Q&A site
・Futoi is used when describing cylindrical or linear objects or shapes.
Example: The line is thick, 'fat' sushi, thick pole, 'fat' person.
・Atsui is used to describe when the width of the direct face of a three-dimensional object is wide.
Example: A thick book, a thick board.
--Basically, when one dimension of an object is wide, 'atsui' is used. When multiple dimensions of an object are wide, 'futoi' is used. It might be easiest to contextualize their respective usages with sentence examples. If you use Shonagon and input '。厚い' (make sure to include the 。) you will find many examples (table, skin, glass, coat of paint, etc.). You can do the same with 'futoi'.
For books like Kanji references the の is usually omitted. For dictionaries of foreign languages the の is often included. Technically, they can be reversed without any misunderstanding, but they have developed this way with dominance of one form versus the other (えいごのじしょ is about twice as commonly used as えいごじしょ）. If Duolingo doesn't accept this form you should probably report it.
As far as the reason the use or non-use of の developed this particular way, your guess is as good as mine.
Why the の is dropped in Japanese is the same reason why "X of Y" becomes "XY" in English.
Consider "the grounds that children play in." People might have said that 1000 years ago. Now, people have had enough and they just say "playground."
Same in Japanese, 「漢字の辞書」might have appeared long ago, but people were too lazy to say the の. For 「英語の辞書」, I guess they don't ask for English dictionaries often enough to drop the の.
Hehe, I only just saw this reply now (eight months late). Made me smile though. :D
I take it you meant:-
I don't think I can top that. I'm guessing the following would be too silly, trying to write modern Japanese grammar in this way:
です and あります are different verbs.
です = it is (a certain way) - in this case, it is thick.
You can say その辞書は厚いです means "that dictionary is thick". Or それは辞書です - "that is a dictionary".
あります = it exists. You'd want to put a particle in front of this.
You can say その辞書はあります - "that dictionary exists". Or その辞書はここにあります - "that dictionary is here".
But I don't think you can mix them. I guess you could say "the thick dictionary is here" - 厚い辞書がここにあります - hopefully this is helpful.