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A guest review by Stelio's son, transcribed and edited by Stelio.

When it comes to shoving movable objects into one's gob, my son is a connoisseur. This weekend he made that great leap that has inspired so many of us: he discovered the joy of polyhedral dice, and he is keen that his observations be shared for the general betterment of society. Altruism: he's too young to know better.

For the purposes of context, let me set the scene for you... Our guide into the oral pleasures of random number generators is an ebullient nineteen-month-old boy. His likes include balloons, balls, his father's animal impressions, and (sadly) kids' TV. His dislikes include illness, turnip, confiscation of interesting objects, and (sadly) nappy changes.

Without further ado, let us plunge into the die by die assessment...


The contenders.


d4

There is a vibrant piquancy to this pyramidal die. Of all the polyhedra on offer, only this aberration lacks parallel planes, making it a singular experience in the oral environment. But that seductive quality is a blatant temptation by what is clearly the darkest of the dice.

Their notorious status as "caltrops" is rivalled perhaps only by the infamous single Lego brick ("Which one day shall be mine; oh yes, it shall be mine."). And when it comes to chewing, their relatively smaller size and streamlined shape make them the easiest to accidentally swallow, and the most likely to stick in your throat and kill you. Beware the d4!

d6

Six-siders are the vanilla of the dice world: common, some would say boring, but successful to an unparalleled degree. The question is: does that success extend also to its masticatory potential?

In a word, no. Don't get me wrong: the d6 has qualities all of its own. The large flat planes are exceptional at channelling drool, offering a high rate of clothes soakage for a minimal chew. But this excess salivation may also lead to the need to suck, and frankly the d6 is just not as exciting as other types of dice.

d8

With the cube's six faces and eight vertices corresponding to the octahedron's six vertices and eight faces, you'd be forgiven for thinking that they offer a similar experience. Not so! The essential flatness of the d6 is lost and replaced by the glorious pointiness of the d8.

The d8 offers paired points in all dimensions, and this makes it wonderful for poking into the cusps of one's deciduous molars. (Premolars? Molars?! Bah! Those are for people with continence.) The d8 offers a quality chew with a delightfully interesting texture.

d10

This stands out as a curious anomaly amongst the other dice: a non-Platonic solid. The pentagonal trapezohedron is at once both round and pointy. While you might think that this offers a taste of both worlds, in fact it fails to deliver the quality of experience that a more specialised shape will bring. Less pointy than the d8 or d4, less round than dice with more faces, the d10 remains a disappointment.

Perhaps my son will return to the ten-sider when, awash with teen hormones, he sees the attraction of the tragically hip angst of the World of Darkness.

d12

Aha! Now you're talking! Leaving behind pointiness, we move onto the rounder dice. As any baby boy can tell you, balls are source of endless fascination and joy (in fact the same opinion may be held be men of any age). Thus the more ball-like the die, the better.

The d12 still retains a pleasant texture for chewing thanks to the angles involved in fitting pentagons together (forget Stelio's ramblings about rhombic dodecahedra; regular dodecahedra are where it's at). This would garner the twelve-sider top marks were it not pipped by higher sided dice...

d20

Yes! Here we have it: the most ball-like of all the standard polyhedral dice. He was hard pressed to choose between the dodecahedron and the icosahedron, but ultimately my son made the simple decision that more sides means rounder, and the better die is the one that's the better ball.

Except... a d20 is mathematically less ball-like than a d12! That may seem counter-intuitive, but here's a table that gives measurable values for the key quality identified by my son: ballosity. Imagine a sphere. Within this sphere place the largest possible polyhedron (of the appropriate shape) that can be wholly contained in it. The proportion of the sphere's volume that is taken up by the polyhedron is its ballosity.

Die Polyhedron Ballosity
d4 regular tetrahedron 12.25%
d6 cube 36.76%
d8 regular octahedron 31.83%
d10 pentagonal trapezohedron 42.30%
d12 regular dodecahedron 66.49%
d20 regular icosahedron 60.55%
d30 rhombic triacontahedron 69.38%

But what's that last row? An interloper?! Gasp!

d30

"Oh, most holy of glories! That such a thing could be! Certainly this is the very epitome of die manufacture, a most-noble heavenly orb fit for the mouths of royal toddlers! When they talk about gem dice, surely this is what they mean!" ...I admit, I'm paraphrasing. His exact words were, "BAW!" (I'm assured that he'll develop the traditional pronunciation of the word 'ball' some time before puberty.)

The d30, or as we more affectionately call it the rhombic triacontohedron, beats all the other dice on two counts: not only does it have a higher ballosity, but also it's bigger. And of course bigger is better. So there you go: big balls are best, and my boy's got 'em.



The winner surrounded by its rivals; note their relative sizes.



Afterthoughts

Don't let your toddler play with dice. Dice are a choking hazard and can kill your child if accidentally swallowed. Stelio is a trained professional. And even he would baulk at babies plus miniature dice.

Beware the Zocchihedron: this d100 is rounder and bigger than any other die noted here. Unless you want to see if your loved one can fit a golf ball in their mouth. At least it will make a great anecdote at the hospital.

Another die that should be popular is the round d6: a perfect ball and it makes a cool rattling sound due to its internal weight (also useful for identifying where in the alimentary canal it is located).



The empirical scientist.

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  • Last edited Sun Apr 3, 2011 1:25 pm (Total Number of Edits: 3)
  • Posted Fri Apr 1, 2011 1:24 pm
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Young & Lawful Good
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For details of the "ballosity" calculations click on any of the individual images of dice above. The calculations are given as comments against the individual images.
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Karl Larsson
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Is this guide valid for cats as well?
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For maximum chewing and slobbering pleasure, and a reduced swallowing hazard, the distinguished connoisseur should consider the jumbo-sized dice:




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U Majuran
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thanks for the cool review but may I point out that you missed a few things:

Toddlers can stick all sorts of things up their ears and noses. Smaller dice would be good candidates.

From a reasonable amount of time in the emergency departement may I point out that the humble D2 (a la the coin) is more commonly swallowed than any of the other die you mentioned put together and you don't need to find it via a 'rattling sound' like the round D6- metal detector and/or X-Ray will do.

And finally - your little one's very cute
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d30? Somebody send that boy a d100!

(And I was really hoping for pics of dice with teeth marks here.)
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DMSamuel
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E Decker wrote:
(And I was really hoping for pics of dice with teeth marks here.)


Me too! I thought I was going to see aftermath dice - with teeth marks, and possibly a video showing an attempt to roll such dice. Perhaps you could train him to put marks in them such that they always roll high?
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Here's a link to nice big squishy 3" foam dice. A small price to pay for toddler curiousity: http://www.thinkgeek.com/geektoys/games/e588/



As for toddler tv, get rid of the television set. Not only will your toddler be better developed by the time he's a teenager, so will your waistline.
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  • Last edited Sun Apr 3, 2011 12:36 am (Total Number of Edits: 1)
  • Posted Sun Apr 3, 2011 12:35 am
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Tongue-in-cheek reponses to tongue-in-cheek comments!

Stelio wrote:
For details of the "ballosity" calculations click on any of the individual images of dice above. The calculations are given as comments against the individual images.
Calculations have been updated to show appropriate workings. These are brief for the platonic solids since they are very simple to calculate, but somewhat more long-winded for the d30 and d10, each of which required further supporting diagrams.

karlkrlarsson wrote:
Is this guide valid for cats as well?
Cats tend to favour dice that roll well, so "ballosity" is a good measure for feline satisfaction as well. Note that the perfect size for a cat would be paw-sized.

Paolo Robino wrote:
For maximum chewing and slobbering pleasure, and a reduced swallowing hazard, the distinguished connoisseur should consider the jumbo-sized dice.
A fine choice, and one that would be very much appreciated by my son! But avoid jumbo metal dice as they are harsh on young teeth.

hydra66 wrote:
Toddlers can stick all sorts of things up their ears and noses. Smaller dice would be good candidates.
Indeed, I can imagine so! I have yet to experience the joys of my children inserting foreign objects into their nasal and aural cavities. Tempting though it is to experiment in that field, I might leave that pleasure to other scientific researchers to report. I wouldn't want to steal all the fun, now!

hydra66 wrote:
From a reasonable amount of time in the emergency department may I point out that the humble D2 (a la the coin) is more commonly swallowed than any of the other die you mentioned put together and you don't need to find it via a 'rattling sound' like the round D6- metal detector and/or X-Ray will do.
Good point, good point! How remiss of me to neglect that worthy though oft-neglected member of the dice family. My focus on the common polyhedral dice has sadly avoided other more esoteric randomisers as well. Unfortunately my son has yet to get his hands on any of these, and I prefer to report from a practical rather than theoretical standpoint. Maybe next 1 April I'll have more to document on the subject?

lorddillon wrote:
E Decker wrote:
(And I was really hoping for pics of dice with teeth marks here.)
Me too! I thought I was going to see aftermath dice - with teeth marks, and possibly a video showing an attempt to roll such dice. Perhaps you could train him to put marks in them such that they always roll high?
Aha! An excellent sentiment. How perspicacious of you to find a way to capitalise on the pure science that I have expounded. I fear that such a project may have limited practical application though: the plastics used in modern dice are sufficiently high quality to resist the relatively feeble mastication of a domestic child. The results of such an investigation would find use with the dice of the 1970s and early 1980s, which are notoriously prone to wear. But the loss of dice heritage in the destructive tests required pose an ethical dilemma for the progressive scientist.

Sam and Max wrote:
Here's a link to nice big squishy 3" foam dice. A small price to pay for toddler curiosity.
Perfect for the safety-conscious parent! An excellent way to not kill your child. Although I suspect that my son would get a lot less joy from trying to chew one of these. Only one way to find out for certain though...
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  • Last edited Mon Apr 23, 2012 12:10 pm (Total Number of Edits: 2)
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Jaime Lawrence
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Have you tried a d16? My 3 year old finds it fascinating.
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Chad Bowser
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My brother, age 1.5 at the time, attempted to ingest a zocchihedron.

While it didn't result in a trip to the hospital, it was a frightening few minutes while my friend held my brother on the ground and I removed the die. My friends and I were terrified. My brother thought it was hilarious (at least he laughed a lot).
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