Righhht… So what permutated form of tetrahedron is that?
Hell, I can call said spaghetti a simple geometric line.
Except for this, except for that.
One may as well try to give a simple geometric definition to a crumpled newspaper.
A bounded surface of genus 0. (Vs. the object in the OP which is a finite, unbounded surface of genus 0.)
Coffee *and * a donut. Yum. 
(Finite, unbounded surfaces of genus 1.)
A topologist is someone who can’t tell his ass from a hole in the ground… but can tell his ass from two holes in the ground.
But he only makes the first error if the hole in the ground goes clean through to the other side of the Earth.
Or, strictly speaking, has a second exit point such as a road tunnel or culvert does.[sub]Explaining jokes really wrecks 'em don’t it? Or is that rectum?[/sub]
A truncated cone, but (for new-school nitpicks) not perfectly formed, to allow for easier handling and more efficient packing.
A century ago, ballplayer Heinie Groh used a “bottle bat”, which was still shaped like a baseball bat (truncated cone), but with an irregularity.
http://blogs.democratandchronicle.com/rochistory/files/2013/10/Heinie-GrohUSE.jpg
Irregular polyhedron … but let’s get back to donut-shaped things … those are my favorite …
Great contribution, unassailable, interesting for itself and what it opens up (“bah”), out of left field. GQ score: 100.
It occurs to me that a long, flat isoceles tetrahedron might actually make a better d4 than the usual design. A regular tetrahedron resting on a table has a vertex at its top rather than a face, and so you have to either label the vertices rather than the faces, or make it so that the face on the bottom is the one that’s selected. (See here for details.) But a long isoceles tetrahedron resting on a table would have one exposed face that is “flatter” than the the other two, and so you could use that as the “selected” face.
Has anyone actually done this, or should I make a quick call to the patent office?
Emphases Mine
Where’s the fourth face?
Yeah, you only have three faces with that design. Seems like if that’s what you’re aiming for, it would be simplest to just use a rectangular prism, like a die stretched so that it could only (with high probability) land on four of the six faces.
Missed edit window –
I retract that. An isosceles tetrahedron would make a fine 4 sided die, but a rectangular prism would work just as well and would be simpler to manufacture. In fact, a prism could be made with any number of sides – 5, 7, 13, etc. which can’t be done with the platonic solids that are usually used. I wonder why D&D players don’t use such dice.
FYI - We’ve had threads and threads on novel dice designs.
The question to the 5-sided polyhedron is whether it would give a 20% probability for each number … and how often is this strictly necessary … as it is each proper dragon die has a pound or two of brass in it, more dice is more weight to lug around … if the situation comes up we can just roll percentage dice … in spite the dangers of throwing five pounds of brass at someone …
Against the table.
And it’s not just isosceles triangles that work, incidentally: You can make a fair d4 from any acute triangle.
But all the same, when I made my own custom dice, I used a dreidle design for the d4 instead of any sort of tetrahedron.
Played around with the shape a bit this weekend. This shows the “stretched pyramid” version versus the “pinched cylinder” version. IMHO they are two different shapes that should have two different names. (Video download link.)
And then immediately gets their posts and accounts deleted, for some reason? What was Fossilene, spammer? sock? spammer of socks?
Great link and, based on your previous vids, probably one well worth seeing. Shame one has to be a member of that site to see it.