# A Non-Platonic Riddle

On the outside I may sound
Like some holy thing.
Paint on me a halo,
Seven colors I require.

Since I'm wrapped around the void,
You may fill me up with air.
while you hold me
in the morning.

You recall they called it all
But impossible but we
all connected
three by three,
you with me.

I can be a real treat for you
(That may sound a little bullish,
but if that should fail to do,
I've a hole inside me too).

I'm looking for a specific single word answer, with explanation of course.

You are a

Torus

On the outside I may sound
Like some holy thing.

Holy sounds like "holey" which a torus is (Thanks Deusovi!)

Paint on me a halo,

Halos are ring-shaped, with some width they'd be torus shaped

Seven colors I require.

You can color a plane with 4 colors (by the four-color theorem), but a graph on a torus needs 7 colors.

Since I'm wrapped around the void,

Referring to the fundamental polygon of a torus being equivalent to wrapping around on both edges?

You may fill me up with air.

You can fill up inner tubes (which are shaped like a torus) with air.

while you hold me
in the morning.

Reference to the coffee mug being topologically equivalent to a torus, which people often hold in the morning?

You recall they called it all
But impossible but we
all connected
three by three,
you with me.

You can't draw a $K_{3,3}$ in a plane (the utilities problem), but you can on a torus?

I can be a real treat for you

Donuts are shaped like tori.

(That may sound a little bullish,

Torus sounds like "Taurus" which is the astrological sign of the bull

but if that should fail to do, I've a hole inside me too).

Tori have a hole in themz

Title:

The torus is not a Platonic solid - for one, it's not convex.

• Gah, beat me to it. For the first two lines, it's either the same as the second-last or something with "holy"/"holey" -- could work either way. – Deusovi May 27 '18 at 4:59
• Also, re the second to last verse, you can remove the question mark... that was precisely what I was going for. – H Walters May 27 '18 at 5:25