Geometric cipher… somehow

I've got a message for you. It's hard to decrypt (I think), but you will like what's said to you. Here's the message:

XXRKUXIQXXXXLLRYIXRVYXIIXPVZXAQKYIXHPSCZWEIJFXGYIXHCHSHGIXXMXIEURIRUEBHIXIXREOXCNLTTTXI

And here are the hints:

Hint 1:

Three. And a bit of int arithmetic being used rarely.

Hint 2:

What are the similarities of A and K or S and J?

• A,K or S,J have no visible similarities if expressed in Ascii,hex,oct,binary ? – firephil Dec 21 '16 at 20:03
• A and K each made of 3-pieces of straight line segments. S and J both contains curve. That may be a similarity; as well op declares it is "geometric puzzle". – Always Confused Jan 27 '17 at 18:09
• @AlwaysConfused Wrong too. U is also in the group of A and K. – Mega Man Feb 4 '17 at 9:10
• A, K and U are letters 1, 11 and 21, all ending in 1. That doesn't work for J and S, though.. – Levieux Feb 4 '17 at 9:15
• @Levieux not on purpose, too. D would be in the same group. Look at the letters itself! – Mega Man Feb 4 '17 at 9:17

Step 1

First, divide the chars in groups of three, like this:

XXR KUX IQX XXX LLR YIX RVY XII XPV ZXA QKY IXH PSC ZWE IJF XGY IXH CHS HGI XXM XIE URI RUE BHI XIX REO XCN LTT TXI

Then, count the axial symmetries on every char and transform the chars to numbers:

220 112 202 222 000 122 011 222 201 021 011 222 001 011 200 201 222 120 202 221 221 102 011 122 222 012 210 011 122

Now, try to see the numbers ternal, with number base 3:

24 14 20 26 0 17 4 26 19 7 4 26 1 4 18 19 26 15 20 25 25 11 4 17 26 5 21 4 17

Now this represents the alphabet, 0-indized, and 26 is space key:

YOU ARE THE BEST PUZZLER EVER
and I made a mistake I didn't notice myself: It resulted in the code for
YOU ARE THE BEST PUZZLER FVER
Sorry. And I am not :)

• I think this would have been impossible to do without any clues and with the current clues. – Techidiot Feb 16 '17 at 19:03
• Difficulty notwithstanding, with some fonts, including this one, K is not perfectly symmetrical about any axis. The difference is slight. Also O, if it is a circle is symmetrical across infinitely many axes. – Matt Feb 16 '17 at 19:05

Some observations:

• There's a total of 87 characters, which can be split op into 29 rows/columns of three (hence the hint maybe?).

• Could the similarities of Hint 2 possibly refer to what these letters are made up of? A and K both consist of 3 straight lines. S and J both consist of one curved line.

• There's lots of X's (and also I's). Most of the I's are next to an X (11 out of 13), so perhaps this is related to Roman numerals??

• Well, the first one is good, but the others aren't really true. – Mega Man Nov 22 '16 at 18:19
• That last line is incorrect, completely. ONLY 1 I can be in front of an X or a V, so the IIX is incorrect. Also the letters, listed in increasing value, are: I, V, X, L, C, D, and M, for 1,5,10,50,100,500,1000 respectively. Also the starting XXXXLL is illegal for 2 reasons: like the above rule, 1 X can only exist before an L or a C, and 2 L's do not make a C. I cannot unfortunately fit all the rules of roman numerals in this comment, but take a look at Wikipedia. – garr890354839 Nov 28 '16 at 17:53
• Frequency analysis to add to this x = 21; i = 13; r = 6; h = 5; e, y = 4; l, t, u, c = 3; p, q, z, g, s, v, k = 2; w, m, f, b, o, i, a, n, d = 1. Also xi(5), ix(7) and xx(4) are the only repeated sequences so look key to this puzzle - probably signifying the type of integer arithmetic to do – DeepPurple Jan 27 '17 at 10:05
• @DeepPurple: your second i should be a j. Also, d doesn't occur at all, it's the only letter that's not in there. – Levieux Jan 27 '17 at 10:52
• @Levieux It wasn't on purpose D isn't there. – Mega Man Feb 4 '17 at 9:11