It looks like it slides more than rolls, maybe having it with equilateral triangles would have been better. Also as you're reading the number on an edge you could put notches along it perhaps.
Inspiring work as ever! I’ve had a similar shape in my dice app for a while now but I never thought to label the edges, or balance it numerically. It’s always a delight to be surpassed :D
I suppose you can do a die with any even number of sides just by having an equator edge and two central vertices where the triangles meet. It would just get harder and harder to read.
The standard 10-sided die uses this form, and the octahedron of the 8-sided die is also equivalent to a bipyramid, so this die is in good company. I haven't seen any dice like this with more sides, but 12 should be easy to do too. It would be fun to have a set of dice following this sequence for as many sides would be practical.
Do you know how long I have been looking for any example of triangular based dipyramid?! Thanks for the cursed dice. I should make a ttrpg that uses your currently “unused” dice.
Is the dihedral angle on the "equator" equal to the dihedral angle on the "meridian"? It should be possible to do, since on an infinitely squished triangular bipyramid the equatorial angle is 0° and the meridial angle is 180°, while on an infinitely stretched one the equatorial angle is 180° and the meridial angle is 60°, so there must be a midpoint where the angles are the same. This could be seen more "fair", since the faces on all 3 sides of the triangle would need the same amount of rotation to come up.
We could have thought about this, but didn't! It looks like squishing the die down just a little bit more gets all of the dihedral angles the same. But it is nice for stacking-like purposes to have each one made from two cube corners.
I would worry that it might not be as readable with pips, since the symbol has to be quite small, and there are two symbols on each face. I don't think I've ever seen a d4 with pips, perhaps for the same reason.
the smaller the angles, the less it rolls, the less useful it is to use dice-towers with them, and the more easy it is to cheat with them. missed opportunity for golden angle equilaterals with side+angle rations 1:1:2 OR 1:2:2
All of the dihedral angles are 90 degrees or more. So you're saying that by this metric this is a better die than the usual d6? (Although this metric also thinks that dice that roll forever, e.g. the d120, are great, which I think not everyone would agree with!) I don't think I follow what a golden angle equilateral is?
@@henryseg oops side ratios are phi ratio, angle ratios are 1:2:2 or 1:1:3 of fifths of a half rotation (*36'/360') . en.wikipedia.org/wiki/Golden_triangle_(mathematics) not too practical for dice, just closer to a pentagon. I once had very round D100 dice with a small metal ball inside them that increases friction and that quickly lowers its center of mass. its is noisy while it is fast, so you can hear where it rolled off the table, and it comes to rest exponential fast and is more stable from tipping over (lower center of mass).
@@ollllj Ah I see. The golden angle (golden ratio in general) is a bit overrated I would say. Best to avoid unless there's a good reason for it to be there in my opinion.
One other thing occurred to me: Why not just use equilateral triangles for the sides/faces? Seems that would be just as (if not more) fair then this design. Still going to plunk at least one of these into my collection though 😃
It would be just as fair with equilateral faces. However, there are other things to optimize for as well. I think that with an equilateral triangles design, it would take a small push to go from one face to its counterpart on the other side of the "equator", in comparison to the push needed to go to one of a face's other two neighbours. With this design, the required pushes are closer. I'm not sure if there's a way to get all of those pushes the same. The look of the die is also important. We 3d printed a few and chose the one we felt looked and rolled best.
Between a cube and these which allows more randomness?? If supposing these are equally weighted, there has to be a statistical variation irregardless of user preference which is truly more random. Hard to explain what I mean. Like how many times they hit a flat surface and bounce up and roll etc is totally relevant in breadth and scale of variation
It looks like it slides more than rolls, maybe having it with equilateral triangles would have been better.
Also as you're reading the number on an edge you could put notches along it perhaps.
0:40 the shade to pyramid D4s, I love it
I actually really like these pyramid shape dice
Inspiring work as ever! I’ve had a similar shape in my dice app for a while now but I never thought to label the edges, or balance it numerically. It’s always a delight to be surpassed :D
Please share the link to your dice app!
(As the channel owner, I can share the link here that Sophie posted on twitter: sophiehoulden.com/dice/)
I suppose you can do a die with any even number of sides just by having an equator edge and two central vertices where the triangles meet. It would just get harder and harder to read.
The standard 10-sided die uses this form, and the octahedron of the 8-sided die is also equivalent to a bipyramid, so this die is in good company. I haven't seen any dice like this with more sides, but 12 should be easy to do too. It would be fun to have a set of dice following this sequence for as many sides would be practical.
@@danl9030
Actually you can get a D20 on his website that uses this same form (I believe as well as a D14).
Because of the edge rounding a D50 is hard to stop and read, but yeah it is a working desing.
Do you know how long I have been looking for any example of triangular based dipyramid?! Thanks for the cursed dice. I should make a ttrpg that uses your currently “unused” dice.
Is the dihedral angle on the "equator" equal to the dihedral angle on the "meridian"? It should be possible to do, since on an infinitely squished triangular bipyramid the equatorial angle is 0° and the meridial angle is 180°, while on an infinitely stretched one the equatorial angle is 180° and the meridial angle is 60°, so there must be a midpoint where the angles are the same. This could be seen more "fair", since the faces on all 3 sides of the triangle would need the same amount of rotation to come up.
We could have thought about this, but didn't! It looks like squishing the die down just a little bit more gets all of the dihedral angles the same. But it is nice for stacking-like purposes to have each one made from two cube corners.
Oh God the skewed cubes are throwing off my brain
Have you considered making child-safe dice, i.e. too big to fit through a 1.25”-diameter hole?
@Henry Segerman I love it 😃. Could you do a version with pips, please?
I would worry that it might not be as readable with pips, since the symbol has to be quite small, and there are two symbols on each face. I don't think I've ever seen a d4 with pips, perhaps for the same reason.
Goodness, every time I see those skewed d6 in motion it really messes with my mind.
the smaller the angles, the less it rolls, the less useful it is to use dice-towers with them, and the more easy it is to cheat with them.
missed opportunity for golden angle equilaterals with side+angle rations 1:1:2 OR 1:2:2
All of the dihedral angles are 90 degrees or more. So you're saying that by this metric this is a better die than the usual d6? (Although this metric also thinks that dice that roll forever, e.g. the d120, are great, which I think not everyone would agree with!)
I don't think I follow what a golden angle equilateral is?
@@henryseg oops side ratios are phi ratio, angle ratios are 1:2:2 or 1:1:3 of fifths of a half rotation (*36'/360') . en.wikipedia.org/wiki/Golden_triangle_(mathematics)
not too practical for dice, just closer to a pentagon.
I once had very round D100 dice with a small metal ball inside them that increases friction and that quickly lowers its center of mass. its is noisy while it is fast, so you can hear where it rolled off the table, and it comes to rest exponential fast and is more stable from tipping over (lower center of mass).
@@ollllj Ah I see. The golden angle (golden ratio in general) is a bit overrated I would say. Best to avoid unless there's a good reason for it to be there in my opinion.
Would you ever consider releasing/selling the CAD/STL files on something like gumroad?
One other thing occurred to me: Why not just use equilateral triangles for the sides/faces? Seems that would be just as (if not more) fair then this design. Still going to plunk at least one of these into my collection though 😃
It would be just as fair with equilateral faces. However, there are other things to optimize for as well. I think that with an equilateral triangles design, it would take a small push to go from one face to its counterpart on the other side of the "equator", in comparison to the push needed to go to one of a face's other two neighbours. With this design, the required pushes are closer. I'm not sure if there's a way to get all of those pushes the same. The look of the die is also important. We 3d printed a few and chose the one we felt looked and rolled best.
I’m not sure about this being more readable…
Between a cube and these which allows more randomness?? If supposing these are equally weighted, there has to be a statistical variation irregardless of user preference which is truly more random. Hard to explain what I mean. Like how many times they hit a flat surface and bounce up and roll etc is totally relevant in breadth and scale of variation
Who’s your dice engraver lol, it’s always such a classic font !
I mostly design the numbers myself in Rhino.
but what about a d4 WITH opposite faces? (d8 with every number twice doesnt count)
Pyramid D6
It's a bit harder to read though
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Dimensions are not the same as the concept of surface...😓😓😓😭😭😭
Not really better. Different. I'd give them a go at least.