by
mctrivia
A die in the shape of the symbol PI. To make it even better this die is perfectly weighted and all sides are roughly the same landing area. If rolled on a flat surface this die will roll fair so you can actually use it.
This die has been tested and found to be fair.
This die has been tested and found to be fair.
by
Magic
Truncated Sphere D11 with 3-fold symmetry.
This die is inspired by the repulsion force polyhedra. Nonetheless, the underlying polyhedron (not rounded) is very different from the shape that can be obtained through this technique with 11 points repulsing each others.
Actually, I calculated the positions of 11 points to have a maximal radius for the circles resulting from the intersection of this underlying polyhedron with a sphere with the following constraints:
- 2 poles (upper and lower face - parallel to the horizontal plane)
- 3 points around each pole
- 3 remaining points corresponding to 3 faces perpendicular to the horizontal plane
The result is a truncated sphere with 11 circular faces of same radius.
It is numbered from 1 to 11: 2 numbers are on faces (poles), 6 between vertices and face and 3 on edges. The sum of the numbers on the 3 upper vertices surronding the North pole is 18. Same thing for the sum of the 3 numbers on the lower vertices surronding the South pole and the sum of the 3 numbers on the edges of the equator.
This die is made of a shell of 1.5mm that contains support material to make it heavier. The engraved numbers have a 0.75 mm depth. They are quite big since they overlap the surrounding faces and thus should be very easy to read.
See this thread for more informations.
Available Truncated Sphere Dice: D4, D6, D8, D9, D10, D%, D11, D12, D14, D15, D16, D17, D18, D20, D24, D32, D33
Alternative shapes: alt D8, 3-fold D10 (rounded), 3-fold D10 (pointed), 4-fold D10, 5-folded D10 (pointed)
Coming soon: D22, D50
Related dice: Concave D4, Concave D6, D4 Shell, D8 Shell.
This die is inspired by the repulsion force polyhedra. Nonetheless, the underlying polyhedron (not rounded) is very different from the shape that can be obtained through this technique with 11 points repulsing each others.
Actually, I calculated the positions of 11 points to have a maximal radius for the circles resulting from the intersection of this underlying polyhedron with a sphere with the following constraints:
- 2 poles (upper and lower face - parallel to the horizontal plane)
- 3 points around each pole
- 3 remaining points corresponding to 3 faces perpendicular to the horizontal plane
The result is a truncated sphere with 11 circular faces of same radius.
It is numbered from 1 to 11: 2 numbers are on faces (poles), 6 between vertices and face and 3 on edges. The sum of the numbers on the 3 upper vertices surronding the North pole is 18. Same thing for the sum of the 3 numbers on the lower vertices surronding the South pole and the sum of the 3 numbers on the edges of the equator.
This die is made of a shell of 1.5mm that contains support material to make it heavier. The engraved numbers have a 0.75 mm depth. They are quite big since they overlap the surrounding faces and thus should be very easy to read.
See this thread for more informations.
Available Truncated Sphere Dice: D4, D6, D8, D9, D10, D%, D11, D12, D14, D15, D16, D17, D18, D20, D24, D32, D33
Alternative shapes: alt D8, 3-fold D10 (rounded), 3-fold D10 (pointed), 4-fold D10, 5-folded D10 (pointed)
Coming soon: D22, D50
Related dice: Concave D4, Concave D6, D4 Shell, D8 Shell.
by
SirisC
A d2 made from the dual of a standard sphereicon. (made from a cylinder instead of a dual-cone) Pips are placed on either side to see the result.
by
pittance
A custom Fisher-Price clockwork record player record - plays "Still Alive" from Portal! The tune and model were all generated in Processing.
Some people have asked for some more details on the way I made the model:
I started with measuring out the discs that came with our player, they're injection moulded and all seem to have quite close tolerances which gave me a great interest in getting the right size for my model.
Once I worked out that it might be possible I moved on to setting up the notes so I could work out a tune. I spent quite a long time with a tone generator and a toothpick (driving my wife half crazy in the process) until I had worked out the frequencies of the notes that the music box part of the player could make. I made the tone generator in Processing using the Beads library.
I found that, although there are 22 separate notes on the music box there are only 16 unique notes, 6 are doubles. I've assumed that this is so that the notes can be played more quickly - due to the mechanism in the player 'tone arm' there's a risk of a missed note or jam if only one track is used and the pips (knobs? dots?) are too close together.
Once I had this information I made Processing sketches (Beads again) to make up new tunes and also check that I had the right notes by playing back one of the existing discs (good job I checked since I had two notes wrong...) with note positions copied from a photo of the disc.
Working out the new tune was complicated since there isn't a full chromatic scale available so some tunes simply can't be played even if you shift the key up and down, I wasn't able to get the rest of the 'Still Alive' tune, for example. The tune repeats twice around the disc and wraps so it keeps playing (for as long as the spring lasts)
Once the tune was done I had to transform from linear note positions which I'd used to work out the tune (the sketch looks like a music stave but with each line being a note on the available scale) into polar coordinates around the disc and verify the dimensions.
I created a blank disc by 'lathing' the vertex-by-vertex profile I measured using vernier calipers around an axis in Processing and exporting it for later use.
The "notes" are added onto the blank disc by compositing some boxes that I generate in Processing from the notes with the pre-rendered disc which is stored as an STL file - here I used the Unlekker library for both export and import/combine/re-export.
Once this is done it can be uploaded directly in Processing to Shapeways.
...and believe it or not that's the short form and entirely skips my (mis)adventures in Blender, Autodesk 123D, Solidworks...
At some point I'd hope to be able to make at least some of the code available but it's in a really bad state at the moment so I'd like to tidy it up before I release anything...
by
Magic
Truncated Sphere D15.
This die is inspired by the repulsive force polyhedra although in this case, the underlying polyhedron (not rounded) is very different from the shape that can be obtained through this technique with 15 points repulsing each others.
Actually, I calculated the positions of points (5 at each tropic, 5 at equator, none at the pole) to have a maximal radius for the circles resulting from the intersection of this underlying polyhedron with a sphere. The result is a truncated sphere with 15 circular faces of same radius.
It is numbered from 1 to 15: all numbers are on edges.
The sum of the numbers on each tropic is 40 and the same applies to the equator.
Except for 8, all the numbers go by pair summing to 16: on the tropic two numbers symmetric relatively to the plane of the equator sum to16 and on the equator circle itself two numbers symmetric relatively to number 8 sum to 16.
This die is made of a shell of 1.5 mm that contains support material to make it heavier. The engraved numbers have a 0.75 mm depth.
More informations in this post.
Available Truncated Sphere Dice: D4, D6, D8, D9, D10, D%, D11, D12, D14, D15, D16, D17, D18, D20, D24, D32, D33
Alternative shapes: alt D8, 3-fold D10 (rounded), 3-fold D10 (pointed), 4-fold D10, 5-folded D10 (pointed)
Coming soon: D22, D50
Related dice: Concave D4, Concave D6, D4 Shell, D8 Shell.
This die is inspired by the repulsive force polyhedra although in this case, the underlying polyhedron (not rounded) is very different from the shape that can be obtained through this technique with 15 points repulsing each others.
Actually, I calculated the positions of points (5 at each tropic, 5 at equator, none at the pole) to have a maximal radius for the circles resulting from the intersection of this underlying polyhedron with a sphere. The result is a truncated sphere with 15 circular faces of same radius.
It is numbered from 1 to 15: all numbers are on edges.
The sum of the numbers on each tropic is 40 and the same applies to the equator.
Except for 8, all the numbers go by pair summing to 16: on the tropic two numbers symmetric relatively to the plane of the equator sum to16 and on the equator circle itself two numbers symmetric relatively to number 8 sum to 16.
This die is made of a shell of 1.5 mm that contains support material to make it heavier. The engraved numbers have a 0.75 mm depth.
More informations in this post.
Available Truncated Sphere Dice: D4, D6, D8, D9, D10, D%, D11, D12, D14, D15, D16, D17, D18, D20, D24, D32, D33
Alternative shapes: alt D8, 3-fold D10 (rounded), 3-fold D10 (pointed), 4-fold D10, 5-folded D10 (pointed)
Coming soon: D22, D50
Related dice: Concave D4, Concave D6, D4 Shell, D8 Shell.
by
clsn
This die is a shell surrounding a chunk of the support material, for cost purposes. It's 3cm in radius, which turns out to be a nice solid size for a die. The numbers look big enough to be readable, and it very decisively lands on a single face with a single face up. A handsome piece of random-number generation!
There's a 4cm version of this too, but I'm starting to think that might be overkill.
There's a 4cm version of this too, but I'm starting to think that might be overkill.
by
loki3
This is a simple 9 sided die.
It's a lat-long polyisohedron, an order 3 polyisohedron. Though this shape has 27 sides, only 9 of them are stable, each of which appear with equal probability. The numbered sides are offset from the other sides so it's easy to read the result of a roll.
Note that this is a blank, so the faces will need to be numbered. For more information on unique dice shapes, see http://loki3.com/poly/fair-dice.html.
It's a lat-long polyisohedron, an order 3 polyisohedron. Though this shape has 27 sides, only 9 of them are stable, each of which appear with equal probability. The numbered sides are offset from the other sides so it's easy to read the result of a roll.
Note that this is a blank, so the faces will need to be numbered. For more information on unique dice shapes, see http://loki3.com/poly/fair-dice.html.
by
Magic
Truncated Sphere D17 with a 5-fold symmetry
This die is inspired by the repulsion force polyhedra. In fact, the underlying polyhedron (not rounded) is very similar to the shape that can be obtained through this technique with 17 points repulsing each others.
Actually, I calculated the positions of 17 points to have a maximal radius for the circles resulting from the intersection of this underlying polyhedron with a sphere with the following constraints:
- 1 point per pole (upper and lower face - parallel to the horizontal plane)
- 5 points around each pole
- 5 remaining points corresponding to 5 faces perpendicular to the horizontal plane
The result is a truncated sphere with 17 circular faces of same radius.
For the numbering, as usual:
- the sum of the 5 numbers of the two tropics and of the equator is constant (and equals to 51)
- the sum of the 2 poles, of two numbers of the tropics that are symmetric relatively to the equator, of two numbers of the equator that are symmetric relatively to number 9 is constant (and equals to 18)
See this thread for more informations.
Available Truncated Sphere Dice: D4, D6, D8, D9, D10, D%, D11, D12, D14, D15, D16, D17, D18, D20, D24, D32, D33
Alternative shapes: alt D8, 3-fold D10 (rounded), 3-fold D10 (pointed), 4-fold D10, 5-folded D10 (pointed)
Coming soon: D22, D50
Related dice: Concave D4, Concave D6, D4 Shell, D8 Shell.
This die is inspired by the repulsion force polyhedra. In fact, the underlying polyhedron (not rounded) is very similar to the shape that can be obtained through this technique with 17 points repulsing each others.
Actually, I calculated the positions of 17 points to have a maximal radius for the circles resulting from the intersection of this underlying polyhedron with a sphere with the following constraints:
- 1 point per pole (upper and lower face - parallel to the horizontal plane)
- 5 points around each pole
- 5 remaining points corresponding to 5 faces perpendicular to the horizontal plane
The result is a truncated sphere with 17 circular faces of same radius.
For the numbering, as usual:
- the sum of the 5 numbers of the two tropics and of the equator is constant (and equals to 51)
- the sum of the 2 poles, of two numbers of the tropics that are symmetric relatively to the equator, of two numbers of the equator that are symmetric relatively to number 9 is constant (and equals to 18)
See this thread for more informations.
Available Truncated Sphere Dice: D4, D6, D8, D9, D10, D%, D11, D12, D14, D15, D16, D17, D18, D20, D24, D32, D33
Alternative shapes: alt D8, 3-fold D10 (rounded), 3-fold D10 (pointed), 4-fold D10, 5-folded D10 (pointed)
Coming soon: D22, D50
Related dice: Concave D4, Concave D6, D4 Shell, D8 Shell.
by
richgain
The Szilassi polyhedron is a seven-sided torus where every face is in contact with all of the other faces, proving that for toroidal topology, 7 different colours are required for a surface map.
This simple little shape is a mathematical curiosity, designed to demonstrate colour printing on the sandstone material. It is also a handy filler for topping those orders up to $25.
PLEASE NOTE:
Following changes to the minimum size requirements for some materials, this model was no longer printable. Consequently, I have now increased the size of the model from 2.5 cm to 4 cm in order to make it printable again.
This simple little shape is a mathematical curiosity, designed to demonstrate colour printing on the sandstone material. It is also a handy filler for topping those orders up to $25.
PLEASE NOTE:
Following changes to the minimum size requirements for some materials, this model was no longer printable. Consequently, I have now increased the size of the model from 2.5 cm to 4 cm in order to make it printable again.
by
DarrenAbbey
