A surprising number of logos have a real map inside them. Not a decorative globe, but an actual projection with an actual graticule, chosen by someone who had to decide where to put the centre and how far out to draw. The flag of the United Nations is the clearest example I know. Take away the olive branches and what is left is a polar azimuthal equidistant map.
So: can that map be rebuilt in GeoCanvas, using only what the app puts in front of a user? Mostly, yes. This is the manual.

What the emblem actually is
The emblem was adopted by the General Assembly in 1946, in Resolution 92 (I). The projection at its centre has one property that matters geometrically and one that matters politically. Geometrically, every straight line drawn from the centre is true to scale, so distance from the pole is simply the radius and the parallels come out as evenly spaced concentric circles. Politically, a pole-centred world puts no country in the middle, which for an organisation of equal member states is close to the point.
Most of the geometry is specified rather than guessed. The official description calls for “a map of the world representing an azimuthal equidistant projection centred on the North Pole… The projection of the map extends to 60 degrees south latitude, and includes five concentric circles.” That fixes nearly everything. Five evenly spaced circles ending at 60°S puts them 30 degrees apart, at 60°N, 30°N, the Equator, 30°S and 60°S, and that outermost circle is the edge of the design, which is the reason step 5 exists. What the description does not give is a meridian count, so the eight spokes, 45 degrees apart, are counted off the artwork.
The build
1Start with Azimuthal Equidistant
In the projections list on the left, under Azimuthal, pick Azimuthal Equidistant. What you get is the right projection in the wrong aspect, centred at 0°N 0°E somewhere in the Gulf of Guinea. Both poles are smeared into the two points where all the meridians converge, top and bottom.
The projection and the aspect are separate choices. Azimuthal equidistant does not mean polar. It means distances from the centre point are true, wherever you put that centre.

2Rotate to the polar aspect, and turn the disc
Click the orientation readout in the bottom bar, the one showing λ 0.0° φ 0.0° γ 0.0°, to open the orientation panel. Drag φ centre down to −90°, then γ roll to 20°.
The three values rotate the globe underneath the projection rather than move a viewpoint over it, which is why the sign looks backwards. To bring the North Pole to the centre you rotate the sphere down by 90 degrees. Once it is there, γ spins the disc about that centre, and 20° brings the Atlantic to the bottom instead of a country, which is roughly how the emblem is turned. Both dials live in the same panel, so there is no reason to do this in two passes.

3Swap in Natural Earth Land
The map opens with World Countries, which draws national borders. The emblem has none, it is a coastline map. In the Layers tab, find Natural Earth Land in Favourites and press Add, then remove World Countries with the bin icon on its row.
Natural Earth Land at 110m is the right level of generalisation here. It has 127 features, coarse enough to read cleanly at logo size, detailed enough that Svalbard and Novaya Zemlya are still recognisable. It is also public domain, which is the other reason it is a good starting point for something you intend to redraw.

4Set the graticule to 45° and 30°
Open Visual Tools and expand Graticule. Set Line spacing to Per axis, then Meridians every to 45° and Parallels every to 30°.
Per axis is the setting that matters here. A single spacing applied to both directions cannot describe this grid: it would give you twelve spokes at 30°, or three circles at 45°, and neither is what is on the flag.

5Stop the grid at 60° south
Still in the graticule panel, switch on Limit extent and set South to −60. Leave West, East and North where they are.
The projection runs all the way to the South Pole, which in this aspect is not a point but the entire outer rim of the disc. Without a limit the meridians keep going and converge again at that rim, the visual opposite of the emblem’s clean outer ring. With the limit set, the 60°S parallel is the last circle drawn and the meridians end on it.

6UN blue on the grid
In the same panel, set Color to #009EDB. That is UN blue as the organisation publishes it in its brand identity guide: Pantone 2925, C80 M20 Y0 K0, R0 G158 B219. Be careful with the value you find elsewhere. #5B92E5 circulates widely as “UN blue” and is not it.

7Make the land editable
Click the layer’s name in the Layers tab to expand its card, then press Copy to editable. The read-only Natural Earth layer is replaced by Copy of Natural Earth Land, carrying all 127 features.
This matters for the next step. Catalogue layers are deliberately immutable, so right-clicking a feature on one shows a Remove entry that is greyed out. Nothing you do can damage the source data. You work on your own copy, and the copy is what the delete acts on.

8Colour the land
On the editable layer’s row, use Edit symbology in Canvas Tools and set the fill Colour to #009EDB. The swatch on the layer row itself opens a gradient picker with no hex field, so the symbology editor is the way in when you want an exact value.
And there is the thick blue band around the rim. That is Antarctica, stretched around the entire circumference. In this projection the South Pole is the outer edge, so a continent sitting on it becomes a ring.

9Delete Antarctica
Right-click anywhere on the outer band and choose Remove. Antarctica is one feature in Natural Earth 110m, so it goes in a single action.
The emblem does not delete Antarctica, of course. It stops the map at 60°S, and Antarctica happens to lie entirely south of that. The result on screen is the same, but the reasoning is different, and it is worth being clear about which one you are doing.

10Clear what is left below 60°S
Antarctica is not the only thing out there. Natural Earth 110m also carries a handful of sub-Antarctic islands, South Georgia and Kerguelen among them, which sit outside the 60°S ring and are not on the emblem. Each one is the same right-click and Remove.
They are small at this zoom, so zoom in before picking them and they come away as easily as Antarctica did. I have left a couple of them in the finished map at the top of this page, because they are a fair picture of what the 110m dataset actually contains down there.

Where the app stops
The emblem’s map is a disc and its olive branches are illustration, and GeoCanvas offers neither a circular crop nor a drawing tool for the wreath.
Why bother
Because the emblem is a real map, and taking it apart shows you the decisions behind it. Where the centre goes. How far out to draw, and who that leaves off. How many spokes. What to do with the continent this projection turns into a ring. Rebuilding it is a quick way to learn what a polar azimuthal equidistant projection does, on an example most people have already seen a thousand times without looking at it.
There are two more logos on my list.
Disclosure
GeoCanvas is not affiliated with, endorsed by, or connected to the United Nations. The UN emblem and flag are protected under Article 6ter of the Paris Convention and UN General Assembly Resolution 92 (I); their use requires UN authorisation. Nothing on this page reproduces the emblem. The map shown is drawn from public-domain Natural Earth data as a cartographic exercise about the azimuthal equidistant projection, and is not a UN product.