My GF is a spy?

Question

So it turns out my long-term girlfriend is a spy.

I probably should have seen the signs earlier (I guess this finally explains all the wigs and false moustaches), but last night she told me on the phone. I feel a bit annoyed, but at the same time I can understand why she couldn't tell me earlier.

Anyway, I went over to her place this morning, she wasn't there and all her stuff was gone.

But here's the weird part, she smashed up the tiles in the bathroom and painted them different colours:

Next to the tiles was this note:

Hey, Sorry I couldn't hang around to welcome you, I had some things to take care of ... far away from here. I've left you instruction saying where to meet, when I'll be there, and what we'll do after you get here.

See you soon. XOXO

PS: When you come can you please bring Baking Soda, Toothpaste and Bleach? Thanks so much.

That was it, so I still have no idea where I'm supposed to go, or when. And I have no idea about what will we do there?

Hint:

The image contains 3 different messages, of length 4, 12 and 3.

Hint:

The note postscript is a hint towards the first message, of length 4. Using the Image Description might be easier for this first step. Uncovering that message will help with the second message.

Hint:

For the first phase, you can ignore the glyphs in the graphic, the colours hide the first cipher. Phew!

Full Image Description:

A 4x3 grid of gray hexagons overlaid with coloured shapes dividing the hexagon into triangular segments pointing to the centre. 
The top-left hexagon has a curved arrow pointing from the top side to the top-right side of the hexagon.

In the first column, the shapes are coloured a dark Red: (#800000)
In the second column, the shapes are coloured Pink (#ff8080)
In the third column, they are bright Yellow (#ffff00)
In the final fourth column, a dark Gold (#808000)

The coloured tiles are:
    
    Top Row:
    
        Hexagon 1: (Top Left): A triangle in the top segment, a Trapezium covering Top-Right, Right and Bottom segments, and finally a diamond covering the bottom left and top left segments.
        Hexagon 2: Blank except for a diamond covering bottom-left and top-left.
        Hexagon 3: A diamond covers the top and top-right segments. A trapezium covers bottom-right, bottom and bottom-left. A triangle in the top-left.
        Hexagon 4: Three triangles in bottom-left, left and top-left.
    
    Middle Row:
        
        Hexagon 1: (Middle Left): Three triangles at top, top-right and bottom-right. A blank space at the bottom, and a diamond covering bottom-left and top-left.
        Hexagon 2: Blank except for a diamond covering bottom-right and bottom.
        Hexagon 3: Triangles at top-right and bottom-right, blank space at the bottom, and a trapezium covering bottom-left, top-left and top.
        Hexagon 4: A diamond covers top-right and bottom-right, a blank space at the bottom, and a trapezium covers bottom-left, top-left and top.
    
    Bottom Row:
        
        Hexagon 1: (Bottom Left): A Trapezium covers top-right, bottom-right and bottom. A triangle is in the bottom-left, and A diamond covers top-left and top.
        Hexagon 2: Blank space at top and top-right, a triangle in bottom-right, and a trapezium covers bottom, bottom-left, and top-left
        Hexagon 3: Blank apart from a single triangle in the bottom-left
        Hexagon 4: A triangle in the top-right, a diamond in bottom-right and bottom, and a trapezium covers bottom-left, top-left and top.

Answer 1

The first step:

The hints explain that we are looking for a four-letter answer that is encoded by the colours of the hexagons.

There are four columns, each in a different colour. The image description helpfully provides the hex codes of these colours: #800000, #ff8080, #ffff00and #808000.

If we look at the individual primary colours, #RRGGBB, we see that there are only three different colour bytes used: 00 (no light intensity), 80 (half intensity) and ff (full intensity). If we treat these as the digits 0, 1 and 2, we now get three ternary numbers: 9, 22, 24, 12.

Converting these numbers to letters via their position in the alphabet (A=1, B=2, ..., Z=26) yields IVXL. These are the first Roman digits.

The second step:

With the hint about Roman numerals, we can now look at each hexagon. The arrow indicates that we should look at the segments clockwise. A triangle means I, a rhomb means V and a trapezium means X. (These figures are made up of one, two or three triangles.) If there is a gap, start there, otherwise, start at the trapezium. We get:



Or, in order:

XVI V XIV III VIII V XII XV XIV IX I XIV

Translated to letters, that is PEN CHELONIAN.

The third step

Chelonians are turtles. Pen and turtle can refer to turtle graphics, where a "turtle" with a pen can be moved across a canvas.

There's still one piece of information in the image that we haven't used: the starting point of the Roman numbers in each hexagon, marked with an orange arrow in the image above.

So here's how it goes: For each of the three lines, put the turtle somewhere, facing to the right. Now determine the angle between the starting point marked with a faint arrow in the original image and the orange arrow that marks the beginning of the Roman-number sequence. (In the first hexagon, that's 60° clockwise.) Turn the turtle about that angle and move forward a constant distance with the pen down.

We'll get:



It spells out w e d.

Where? When? What?

"I've left you instruction saying where to meet, when I'll be there, and what we'll do after you get here", she said. Well ...

We'll meet in WED: in Wedau Airport in Papua New Guinea, "far away from here".
She'll be there on Wed: on Wednesday.
And we'll wed each other: we'll get married.

I'm excited! She'll look stunning in her white dress, pink wig and twirly stick-on moustache.