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Shapeways: Bring your creativity to life in 3DNew Dice
http://www.shapeways.com/forum/index.php?t=rview&goto=19911&th=3847#msg_19911
<![CDATA[Hi all,<br />
<br />
As discuss in the topic "Designing dice for dice snobs", I designed today a new <a href="http://www.shapeways.com/model/171149/" target="_blank">Average D6</a> where you have to make the average of 4 faces of an octahedron, to find the result of a regular D6.<br />
<a href="http://www.shapeways.com/model/171149/" target="_blank"><img src="index.php?t=getfile&id=5704&private=0" border=0 alt="index.php?t=getfile&id=5704&private=0"></a><br />
The faces of the octahedron are numbered 1, 1, 1, 1, 2, 4, 8, and 10.<br />
Here are the operations :<br />
<font face="Courier">(1 + 1 + 1 + 1)/4 = 4/4 = 1<br />
(1 + 1 + 2 + 4)/4 = 8/4 = 2<br />
(1 + 1 + 2 + 8)/4 =12/4 = 3<br />
(1 + 1 + 4 +10)/4 =16/4 = 4<br />
(1 + 1 + 8 +10)/4 =20/4 = 5<br />
(2 + 4 + 8 +10)/4 =24/4 = 6</font><br />
<br />
The positions of the virtual 1, 2, 3, 4, 5 and 6 are the regular positions of a D6 (opposite sides sum to 7).<br />
This die is 21.5 x 21.5 x 21.5 mm. The diameter of the wire of the frame is 3 mm so you can print it in Stainless Steel. The price will be less than $25.<br />
<br />
It has not been prototyped yet (as soon as I will do, it will be in the "It arrived" section).<br />
<br />
More informations soon about other variations of this design.<br />
<br />
[EDIT]<br />
if you choose 1, 1, 1, 1 for the four upper faces of the octahedon, you still have several choices for the lower faces (all numbers being larger or equal to 1):<br />
- 1, 5, 9, 9 (all numbers are in the form 4k+1, but I did not choose this one because 1 is repeated again and 9 appears twice)<br />
- 2, 4, 10, 8 (opposite numbers sum to 12, the one I chosed)<br />
- 3, 3, 11, 7 (all numbers are in the form 4k+3 unlike the four 1 of the opposite faces, I did not chose this one also because 3 appears twice)<br />
- 4, 2, 12, 6 (I prefered the other one because the maximum number is smaller)<br />
- 5, 1, 13, 5 (all numbers are in the form 4k+1, I did not choose this one because 1 is repeated again and 5 appears twice)]]>Magic2010-10-31T15:26:44-00:00Re: New Dice
http://www.shapeways.com/forum/index.php?t=rview&goto=19912&th=3847#msg_19912
<![CDATA[And here is the first variation: the <a href="http://www.shapeways.com/model/171178/" target="_blank">4-Letter Words Die</a>.<br />
The same design but with letters instead of numbers.<br />
The goal this time is to use the four letters of the upper faces of the octahedron to form a word.<br />
<br />
<a href="http://www.shapeways.com/model/171178/" target="_blank"><img src="index.php?t=getfile&id=5705&private=0" border=0 alt="index.php?t=getfile&id=5705&private=0"></a><br />
I spent some time to find nice combinations. Probably there are better results, but on my side, with the letters I used, I got this words:<br />
- MAIL / LIMA / MALI<br />
- LION / LOIN<br />
- COLA / COAL<br />
- MACE / CAME<br />
- CONE / NOCE<br />
- MINE / MIEN<br />
<br />
I choose those words, not only because they have anagrams, but also because they make sense in English and in French (at least one by line).<br />
<br />
Here is the scheme of the positions of the letters (one letter at each corner of a cube):<br />
<font face="Courier">I . . L<br />
. N O .<br />
. E C .<br />
M . . A</font><br />
<br />
And here are some not as good (according to me) solutions:<br />
<font face="Courier">E . . N | S . . T<br />
. L I . | . L A .<br />
. S P . | . E R .<br />
O . . T | O . . M</font><br />
<br />
Can you find better solutions?<br />
Perhaps by allowing W = M, U = C and N = Z?]]>Magic2010-10-31T15:56:58-00:00Re: New Dice
http://www.shapeways.com/forum/index.php?t=rview&goto=19947&th=3847#msg_19947
<![CDATA[Wow... I've seen that someone ordered my dice before I had the opportunity to do so! Thanks!<br />
<br />
I was actually busy with the next member of the average family: the <a href="http://www.shapeways.com/model/171676/" target="_blank">Average D8</a>.<br />
<a href="http://www.shapeways.com/model/171676/" target="_blank"><img src="index.php?t=getfile&id=5711&private=0" border=0 alt="index.php?t=getfile&id=5711&private=0"></a><br />
<br />
It's a cube inserted inside a framed octahedron.<br />
This time, you have to make the average of 3 faces of the inner cube (sharing a common vertex pointing upside) to find the result of the D8.<br />
<br />
The face of the inner cube are numbered 1, 1, 1, 4, 7 and 13. The solution is unique (as far as I can see).<br />
<br />
The calculations are:<br />
<font face="Courier">(1 + 1 + 1)/3 = 3/3 = 1<br />
(1 + 1 + 4)/3 = 6/3 = 2<br />
(1 + 1 + 7)/3 = 9/3 = 3<br />
(1 + 4 + 7)/3 =12/3 = 4<br />
(1 + 1 +13)/3 =15/3 = 5<br />
(1 + 4 +13)/3 =18/3 = 6<br />
(1 + 7 +13)/3 =21/3 = 7<br />
(4 + 7 +13)/3 =24/3 = 8</font><br />
<br />
The position of the results from 1 to 8 are nearly those of one of my standard D8, only the 7 and the 5 (and their opposite faces) being swapped.<br />
Anyway, I am unsure there is a real logic in the D8 numbering (except opposite faces sum to 9), so this one - which has an underlying explanation - could be adopted.<br />
<br />
Concerning the Average D20 and most of all for the Average D12, the calculations will be far more complex, so do not expect them too soon.<br />
There are perhaps more chance to see the 5-letter words D12...]]>Magic2010-11-01T22:33:47-00:00Re: New Dice
http://www.shapeways.com/forum/index.php?t=rview&goto=20000&th=3847#msg_20000
<![CDATA[Hi again,<br />
<br />
I would like to introduce an unexpected member of the Average Dice family: the <a href="http://www.shapeways.com/model/172068/" target="_blank">Average D4</a>.<br />
<br />
But before that I would like to share how I constructed it, so sorry for the long post (and for those bored by pseudo-mathematical explanations, just skip to the picture <img src="http://www.shapeways.com/forum/images/smiley_icons/icon_smile.gif" border=0 alt="Smile">)<br />
<br />
<font color="green">/* begin mathematical blabla */</font><br />
I knew it was impossible to follow exactly the same rules to make an average D4, because if the result 1 is made by averaging 1s then 3 faces out of 4 should have been numbered 1 and only one face was remaining. This would have given the expected 1 and 3 times another result.<br />
But by bending the rules, by allowing 0 or even negative numbers, I was convinced I could reach the goal of having 4 numbers that taken 3 by 3 could average to 1, 2, 3 and 4.<br />
I tryed using 0, then -1 and also -2, but arrived nowhere.<br />
<br />
So to start with something, I took a D4 numbered for 1 to 4 and I summed the faces sharing one vertex<br />
<font face="Courier">1+2+3=6<br />
1+2+4=7<br />
1+3+4=8<br />
2+3+4=9</font><br />
The interesting thing was that those results were following each other: 6, 7, 8, 9. But I had to substract 5 to those results to obtain was I wanted.<br />
I could not lower the face numbers by 1 (these would have lowered the result by only 3). To achieve the result I have to substract from the initial a fractional number: 5/3<br />
<font face="Courier">1 - (5/3)=-2/3<br />
2 - (5/3)= 1/3<br />
3 - (5/3)= 4/3<br />
4 - (5/3)= 7/3</font><br />
By replacing 1 by -2/3 2 by 1/3 etc... I could obtain by summing 1, 2, 3, 4. But as it is not a summing die, but an average die, I precisely had to multiply these number by 3 since the average is made by summing 3 numbers and then dividing them by 3.<br />
That's how the numbers -2, 1, 4 and 7 appeared to me.<br />
<font color="green">/* end mathematical blabla */</font><br />
So, here it is:<br />
<a href="http://www.shapeways.com/model/172068/" target="_blank"><img src="index.php?t=getfile&id=5723&private=0" border=0 alt="index.php?t=getfile&id=5723&private=0"></a><br />
No need to add any frame: when lying on a flat surface, the tetrahdron has already a vertex pointing upward.<br />
So you just have to sum the numbers of the 3 visible faces.<br />
As said earlier, these numbers are -2, 1, 4 and 7.<br />
<br />
The operations you have to do are:<br />
<font face="Courier">(-2+1+4)/3 = 3/3 = 1<br />
(-2+1+7)/3 = 6/3 = 2<br />
(-2+4+7)/3 = 9/3 = 3<br />
( 1+4+7)/3 =12/3 = 4</font><br />
<br />
Are there other solutions for numbering the faces?<br />
<br />
[EDIT: fixed some wrong maths]]]>Magic2010-11-03T07:03:57-00:00Re: New Dice
http://www.shapeways.com/forum/index.php?t=rview&goto=20022&th=3847#msg_20022
<![CDATA[Stop with the math already <img src="http://www.shapeways.com/forum/images/smiley_icons/icon_razz.gif" border=0 alt="Razz">. Your last two solutions you have 3/3 = 3 and 3/3 = 4. ]]>Youknowwho4eva2010-11-03T12:55:05-00:00Re: New Dice
http://www.shapeways.com/forum/index.php?t=rview&goto=20024&th=3847#msg_20024
<![CDATA[Oh. So, someone read it <img src="http://www.shapeways.com/forum/images/smiley_icons/icon_biggrin.gif" border=0 alt="Very Happy"><br />
I am going to fix that! Thanks!]]>Magic2010-11-03T13:11:06-00:00Re: New Dice
http://www.shapeways.com/forum/index.php?t=rview&goto=20025&th=3847#msg_20025
<![CDATA[Yea I read <img src="http://www.shapeways.com/forum/images/smiley_icons/icon_rolleyes.gif" border=0 alt="Rolling Eyes"> it lol. I don't know why it caught my eye but it did. I like the Outside the box thinking of these. ]]>Youknowwho4eva2010-11-03T13:17:52-00:00Re: New Dice
http://www.shapeways.com/forum/index.php?t=rview&goto=20027&th=3847#msg_20027
<![CDATA[Interesting stuff! But what about the icosahedron / dodecahedron?? Have you gotten that to work out?? <img src="http://www.shapeways.com/forum/images/smiley_icons/icon_biggrin.gif" border=0 alt="Very Happy"> ]]>gibell2010-11-03T13:40:00-00:00Re: New Dice
http://www.shapeways.com/forum/index.php?t=rview&goto=20053&th=3847#msg_20053
<![CDATA[@gibell Ahah! Is that a challenge?<br />
I am currently working on Average D20 and Average D12.<br />
On Average D20, I can already tell you that the numbers on the 12 faces of the internal dodecahedron will be multiples of 3 plus 1 (numbers like 1, 4, 7, 10, 13, 16, 19...) and the 12 of them will sum up to 126.<br />
<br />
And BTW, for Average D4 the solution is unique, and can be found just resolving a system of equations.<br />
<br />
[EDIT] the sum must be 126, that is 210 (the sum of the numbers from 1 to 20) multplied by 3 (the number of faces joining into a vertex) divided by 5 (the number of vertices by face).]]>Magic2010-11-03T19:52:51-00:00Re: New Dice
http://www.shapeways.com/forum/index.php?t=rview&goto=20181&th=3847#msg_20181
<![CDATA[I tried to found manually the solutions for the average D20, but each time I thought I got the solution, I was missing it by one number (for instance, all the numbers between 1 and 20 were present except for 17 that was replaced by 22!).<br />
<br />
So I decided to use my computer to enumerate part of the combinations, and I found 5 distinct solutions.<br />
3 solutions use the numbers 1-1-1-4-4-7-10-13-16-22-22-25 in the internal dodecahedron's faces, 1 solution the numbers 1-1-1-4-4-10-13-16-16-19-19-22 and the last one the numbers 1-1-1-4-7-7-13-13-19-19-19-22.<br />
<br />
I think I will use the last one because there are three 19s at one vertex (that average to 19!) and it's a kind echo to the three 1s.<br />
<br />
Unfortunately none of the solutions respects the property that opposite faces of the framed D20 sum to 21...<br />
<br />
Now the D12... <img src="http://www.shapeways.com/forum/images/smiley_icons/icon_biggrin.gif" border=0 alt="Very Happy"> ]]>Magic2010-11-06T21:47:11-00:00Re: New Dice
http://www.shapeways.com/forum/index.php?t=rview&goto=20218&th=3847#msg_20218
<![CDATA[Ask Shapeways to add a Casio FX calculator to each dice sale !!! <img src="http://www.shapeways.com/forum/images/smiley_icons/icon_razz.gif" border=0 alt="Razz"> <br />
<br />
]]>dizingof2010-11-08T11:01:22-00:00Re: New Dice
http://www.shapeways.com/forum/index.php?t=rview&goto=20651&th=3847#msg_20651
<![CDATA[The Average Dice are really interesting. So expect more messages from me in this thread! <img src="http://www.shapeways.com/forum/images/smiley_icons/icon_biggrin.gif" border=0 alt="Very Happy"> <br />
I solved the Average D20 and the Average D12 seems much easier, but I had a problem with the design.<br />
So I decided to use 3 "form factors" for the Average Dice<br />
<img src="index.php?t=getfile&id=5952&private=0" border=0 alt="index.php?t=getfile&id=5952&private=0"><br />
I called the one you already seen for the <a href="http://www.shapeways.com/model/171149/" target="_blank">D6</a> and the <a href="http://www.shapeways.com/model/171676/" target="_blank">D8</a> "Cage"<br />
And beside it, you have the <a href="http://www.shapeways.com/model/175051/" target="_blank">"Molecule" one</a> and the <a href="http://www.shapeways.com/model/177503/" target="_blank">"Hollow" one</a>.<br />
I will probably use the Molecule design to make the D12 and the D20 (with no need to repeat the numbers as I did for the Average D6 Molecule).<br />
The Hollow one can be used for D6 and D8 only, I guess. The big hole at the center of each face underline the fact that there is no number where usually you can find one.<br />
<br />
More news soon...<br />
Stay tuned!]]>Magic2010-11-17T22:00:34-00:00Re: New Dice
http://www.shapeways.com/forum/index.php?t=rview&goto=21002&th=3847#msg_21002
<![CDATA[I was working on the Average-D12, and I realized that it can be a little bit "boring", since it contains only numbers in the form 5k+1 (like 1, 6, 11, 16 etc.). So you have to sum three 6 and two 1 to obtain 20 and then divide by 5 to get the result (4).<br />
<br />
That's why I was wondering if I could transform an Average-Die into a Sum-Die (where you would have only to sum the numbers written on the faces around a vertex, without dividing by the number of face, which imply that the numbers will be smaller).<br />
<br />
An obvious way to do that is to divide from the beginning all the numbers by the number of faces by vertex.<br />
For instance, for the D6 with the numbers 1, 1, 1, 1, 2, 4, 6 and 10, if you divide by 4 you obtain 1/4, 1/4, 1/4, 1/4 1/2, 1, 3/2 and 5/2. This does not change the results that go from 1 to 6. With these fractional numbers, you obtain what we can call a <b>fractional Sum-D6</b>.<br />
<br />
Another way would be to use numbers in the form <i>4k+1</i> like 1, 1, 1, 1, 1, 5, 9, 9 and replace <i>4k+1</i> by simply <i>k</i> that is 0, 0, 0, 0, 0, 1, 2, 2.<br />
By summing, you obtain all the numbers from 0 to 5 (instead of 1 to 6): this is the <b>integer Sum-D6</b>.<br />
You can do it with any regular Average-Die.<br />
For instance for the Average-D4 (-2, 1, 4, 7) the transformation leads to the numbers -1, 0, 1 and 2 and taken 3 by 3 their sum gives all the numbers between 0 and 3.<br />
<br />
This is the first step to my next post: the Double-D6!<br />
<br />
]]>Magic2010-11-27T08:04:31-00:00Double D6
http://www.shapeways.com/forum/index.php?t=rview&goto=21003&th=3847#msg_21003
<![CDATA[OK, after the starter, the main course!<br />
<br />
There are several <a href="http://www.dicecollector.com/THE_DICE_THEME_DOUBLE.html" target="_blank">double dice</a> but I wanted to try something new.<br />
<br />
So I dediced to combine a "nearly" standard D6 with an integer Sum-D6 to make a <a href="http://www.shapeways.com/model/181549/" target="_blank">Double-D6</a>.<br />
<br />
<a href="http://www.shapeways.com/model/181549/" target="_blank"><img src="index.php?t=getfile&id=6064&private=0" border=0 alt="index.php?t=getfile&id=6064&private=0"></a><br />
<br />
For the integer Sum-D6 that make the frame, I chose the number 0, 0, 0, 0, 0, 1, 1 and 3 because, for aesthetical reasons, I wanted to avoid the number 2 (impossible to place 2 pips symmetrically in a corner).<br />
<br />
The core is a D6 that is numbered from 2 to 7, to compensate the fact that the frame goes only from 0 to 5 (instead of 1 to 6, as regular D6).<br />
<br />
The core can roll freely inside the frame, so when you draw this die, the frame and the core both get a random orientation and the result when you sum the pips from the upper face of the core and the pips of the 4 upper corners of the frame is the same as summing 2 regular D6.<br />
For instance, in the picture, you have 3 pips on the face and 2 extra pips in the corners thus the result is 5.<br />
<br />
So instead of using 2 regular D6, if you do not care about individual results but only the sum, you can use this <a href="http://www.shapeways.com/model/181549/" target="_blank">Double-D6</a>. Same results but in a more original and stylish way! <img src="http://www.shapeways.com/forum/images/smiley_icons/icon_biggrin.gif" border=0 alt="Very Happy"><br />
<br />
It has not been prototyped yet so I am unsure it rolls properly. But I will order a version in Alumide soon.<br />
<br />
]]>Magic2010-11-27T08:53:49-00:00Re: Double D6
http://www.shapeways.com/forum/index.php?t=rview&goto=21561&th=3847#msg_21561
<![CDATA[The <a href="http://www.shapeways.com/forum/index.php?t=msg&goto=21560&#msg_21560" target="_blank">D4, D6 Cage and D8 Cage arrived</a>!]]>Magic2010-12-12T17:23:00-00:00Re: Double D6
http://www.shapeways.com/forum/index.php?t=rview&goto=21568&th=3847#msg_21568
<![CDATA[that is a really cool design.]]>mctrivia2010-12-12T20:44:21-00:00Re: Double D6
http://www.shapeways.com/forum/index.php?t=rview&goto=21570&th=3847#msg_21570
<![CDATA[Thanks Mctrivia,<br />
<br />
D12 and D20 should follow (probably in the molecule form factor), but I am currently busy with some truncated spheres <img src="http://www.shapeways.com/forum/images/smiley_icons/icon_wink.gif" border=0 alt="Wink">]]>Magic2010-12-12T20:50:55-00:00Re: Double D6
http://www.shapeways.com/forum/index.php?t=rview&goto=21572&th=3847#msg_21572
<![CDATA[i would print a test before you waist time designing them. I will definitely be buying at least 1 if this will pass chi square test but i suspect it will not. Not because your math is off your theory is sound. Just suspect the last state the die was in will add a biais to the next state.<br />
<br />
That said I am sure some will buy if fair or not. but if you test you may be able to figure out how to improve and make both fair and beautiful.]]>mctrivia2010-12-12T22:11:56-00:00