Talk:Zocchihedron

I have added some information from White Dwarf magazine detailing the results of the test. Mill's test on the Zocchihedron gave a result of 34 more often than any other, but in the range of 10-90 the distribution was largely fair.

Does anyone have information on the fairness of more recent Zocchihedra? --Azezel 14:33, 18 Jul 2006 (UTC)

JavBol, we do not "correct" the wording of others' signed remarks. Azezel wrote "Mill's test Zocchihedron", presumably meaning the instance of Z. that Mill obtained and tested, rather than Mill's test on the Platonic ideal Z. —Tamfang (talk) 01:41, 13 July 2023 (UTC)

@Tamfang: Thank you for your explanation of Azezel's phrasing. As for the ideal 100-faced actual polyhedron corresponding to the ideal Zocchihedron, I guess you know it is not a Platonic solid. 🙂 —JavBol (talk) 00:05, 15 July 2023 (UTC)

Heh, right, that sense did not occur to me, I was thinking of Platonic ideal. —Tamfang (talk) 00:08, 15 July 2023 (UTC)

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Why the quotation marks around "invented"? There's nothing on this page or Lou Zocchi's that seems to justify them. Eurleif 17:46, 17 Jun 2004 (UTC)

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…not a polyhedron [but] more like a ball with 100 flattened planes...

All right, that piques my curiosity. Does the author mean that the Zocchihedron is not a regular polyhedron, or that it also has non-flattened planes like an ordinary die? Or something else altogether? A picture would be interesting…
—Herbee 12:23, 15 Sep 2004 (UTC)

I wish I had a digital camera to give you a good photo, but here's a quick set of results from Google. Think golfball and you'll be in the right place. Here's Zocchi's patent application - it's got a decent diagram. --Rossumcapek 22:46, 17 Sep 2004 (UTC)

Since the above link isn't working for me today, I used a similar patent search to find these patents:

• Patent 6,926,276 Braking system for dice
• Patent 6,926,275 Five sided dice
• Patent D303,553 Spherically shaped game die

Would it be appropriate for this article to link directly to these patents?

To answer the original question, perhaps the article description should be more like:

The Zocchihedron has one non-flat surface (the surface of a sphere), and 100 "spots". Each spot is flat and isolated from all its neighboring spots (and so is therefore a circle). Each of the 100 spots is the same size as all the other spots.

(The spots look like they are dimpled in concave slightly -- is that just an optical illusion?)

Unfortunately, it is not mathematically possible to place 100 points on a sphere perfectly evenly, although one can get pretty close. It *is* possible to place 120 points on a sphere perfectly evenly, making a dice shaped like a disdyakis triacontahedron. Mathpuzzle has a complete list of all possible Fair Dice with nice pictures; and Klaus Æ. Mogensen has more details on them.

--68.0.120.35 17:04, 9 January 2007 (UTC)

Actually:

• The surface of the Zocchihedron is non-polyhedral, but is not a sphere either: it's a flattened sphere, at 100 "spots". Not all its 100 spots are disks. Its 100 spots have several different shapes & several different areas. (The Zocchihedron has a lot of chamfer. Now, on Google, see pictures of 100-sided dice corresponding to the same 100-faced actual polyhedron as the Zocchihedron does, but with very little chamfer, almost like the 100-faced actual polyhedron in question: this has not enough regularity to have an intersphere. So, spherically chamfering this polyhedron won't make a die with disk sides.)
• It is mathematically possible to place 100 points on a sphere perfectly evenly:
  • On the vertices of a uniform 50-gonal prism; this has 50 square "lateral" faces & 2 regular (50-gonal) "basal" faces. (The original sphere is the circumscribed sphere of this prism.) But obviously, not all the faces of this prism are even. Still, this will make a fair 50-sided die.
  • Or on the vertices of a uniform 50-gonal antiprism; this has 100 equilateral triangle "lateral" faces & 2 regular (50-gonal) "basal" faces. (The original sphere is the circumscribed sphere of this antiprism.) But obviously, not all the faces of this antiprism are even. Still, this will make a fair 100-sided die.
• It is mathematically possible to place 100 faces on a sphere perfectly evenly: the 100 equivalent isosceles (or scalene) triangle faces of a right 50-gonal (or convex right di-25-gonal) bipyramid (or right di-25-gonal scalenohedron), or the 100 equivalent kite faces of a right 50-gonal trapezohedron. (The original sphere is the inscribed sphere of these 3+1 polyhedra.) These 3+1 polyhedra will make fair 100-sided dice.
• It is possible to place 120 faces on a sphere perfectly evenly, making a disdyakis triacontahedron. 🙂

—JavBol (talk) 19:21, 12 June 2023 (UTC)

A nonuniform right prism or antiprism has the same symmetry, assuming the base is regular. —Tamfang (talk) 01:48, 13 July 2023 (UTC)

Yes, indeed, it is mathematically possible to place 100 points on a sphere less evenly:

• On the vertices of a nonuniform right 50-gonal prism with 2 regular (50-gonal) "basal" faces; this has 50 rectangle "lateral" faces. (The original sphere is also the circumscribed sphere of this prism.) But obviously, not all the faces of this prism are even. Still, this will also make a fair 50-sided die.
• Or on the vertices of a nonuniform right 50-gonal antiprism with 2 regular (50-gonal) "basal" faces; this has 100 isosceles triangle "lateral" faces. (The original sphere is also the circumscribed sphere of this antiprism.) But obviously, not all the faces of this antiprism are even. Still, this will also make a fair 100-sided die.

—JavBol (talk) 00:05, 15 July 2023 (UTC)

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Does anyone know where to find the frequency distribution test results?

I have Mills own distribution chart (from which I took the information I put in the article) - but I do not hold the copyright obviously, so I am unwilling to publish it. Suffice it to say that it was more or less fair in the range between 10 and 90.

--Azezel 11:48, 8 Aug 2006 (UTC)

I believe that the sample size of 5164 for the frequency distribution is much too small to make a determination about fairness. I can't provide a detailed argument at the moment, but running a simulation with a random number generator in Mathematica gives: 86 was rolled 34 times, 75 was rolled 38 times, ..., 80 was rolled 65 times, 100 was rolled 66 times. And that hardly seems like an even distribution, though I'm confident that it is. Gabrielgauthier (talk) 07:03, 5 May 2015 (UTC)

Purchasing?

Where can I get one of these?

The internet - I won't advertise any comercial sites, but a web search will yeild several results. --Azezel 11:48, 8 Aug 2006 (UTC)

I beg to differ.. I googled this and it seems nobody sells these. So is this just a one-&-done experiment? why a whole wiki-page if you can't find even one shopping page, and inconclusive results 12.251.225.250 (talk) 15:54, 1 December 2013 (UTC)?

A 'basic' concept for a zocchihedron.

Although from the picture it seems that the edges aren't triangular, surley a zoccihihedron can be easily visualised or even created by splitting the faces of a tetrahedron into 25 equilateral triangle faces and then inflating into a spherical shape? Robo37 (talk) 10:44, 29 November 2011 (UTC)

how deep should the water be?

Zocchi discovered that the die would perform best at a depth of 13.85 mm, so it floats.

What does 'depth' mean here? How does that make it float? —Tamfang (talk) 05:15, 23 January 2013 (UTC)

For that matter, what is it "floating" in? The whole sentence is confusing and seems out of place. --Hatster301 (talk) 13:24, 23 January 2013 (UTC)

This must be wrong. If the die floated it would never settle. — Frayæ (Talk/Spjall) 21:29, 9 September 2018 (UTC)