ALIA IACTA EST
"Mit den Fursten der Finsternis habe ich Wurfel gespielt."
Thanks to Lawrence Maynard's article "What is Dice 'Fairness' Anyway?" here's the argument for the acceptance of a non-isohedron like the Trapezohedron as a "fair die:" ` ` (Although) it's actually a dual polyhedra shape that doesn't satisfy the conditions to make it an isohedron (it doesn't have the perfect reflectional symmetry required), ... it does meet the requirements of the Euler polyhedral formula (...for any convex polyhedron, the number of vertices and faces together is exactly two more than the number of edges...) V = 12, N = 10, E = 20 so 12 + 10 = 20 + 2. ' '
But, when it comes to polyhedral dice, i have always considered the "Pentagonal Deltahedron-like" Trapezohedral d10 to be somewhat of an aberration.
According to this esssay on the "Properties of Dice," by Klaus Æ. Mogensen, "the d10 technically belongs to a special case of an infinite series where (the number of sides and corners is four)."
But in general, when it comes to using dice modelled after the Platonic solids, i prefer the "regular convex polyhedra."
So, when using dice for decimal functions, i think that it's best to use those based on the icosahedron.
...And yes, that advice applies even for percentile determination!
For one thing, it's just really difficult to get reliably satisfactory results from dice in the form of a trapezohedron (and icosahedrons are the bomb, anyway!).
The icosahedron can also be used to make awesome images, which many people are already familiar with through M.C. Escher's wood engraving, "Stars".
With all due respect to those of you who appreciate the Storyteller system, i would even prefer to use the rock-paper-scissors (RPS) system of Mind's Eye Theater (or, how about: Rock, Paper, Scissors, Spock, Lizard!!!?!!?!?!), rather than be forced to use the d10.
...Back in the day, the d20 was numbered 0-9 twice ("d20 ... 0-9 X 2"), and you had to actually ink in one set of the numbers by hand to use it as a d20... or roll a second die high/low to determine if the d20's result was in the ones' or tens' digit... and then came the the d20+, which came with little inscriptions of a "+" so that you didn't even have to ink half of the die.
Eventually, the d10 was produced, and d20s began to be produced with the numbers 1-20.
If i must use d10s, then they had better have been manufactured with Precision Edges™ for improved accuracy, like all of the dice from Gamescience! (for comparison, here's a photo of d10s with rounded edges from Crystal Caste)
Although i respect Louis Zocchi (for his historical and strategic knowledge, unique wit, and his support of gaming throughout the years), and Gamescience (for producing superior quality dice in general), i think the Zocchihedron's ultimate value is in comic relief.
In, "The Haunter of the Dark," H.P. Lovecraft even mentions the existence of an artifact of extreme evil, The Shining Trapezohedron (which is the Four of Artifacts in the The Lovecraft Tarot by D.L. Hutchinson). So, playing Call of Cthulhu with Trapezohedrons is probably just asking for trouble (btw, i have updated the Lovecraftian gaming section, in my previous "Intro to Lovecraft" post). Some people have suggested that the Shining Trapezohedron may be the same relic known as The Chintamani... but at press time of this article, Mushika Metamorphose (our closest correspondant to the source), had been unable to confirm or deny this rumor, even through scrying methods, using the jewel as a prism. The only response from the aethyrs was from an elusive icosahedron which repeatedly stated the cryptic message, "Reply hazy, try again." Maybe implementation of the stone as a gate will provide further elucidation? In the meantime, one may consider consultation with the Order of the Trapezoid, a chivalric order of knighthood within the Temple of Set. According to their original Mission statement, "inspired by a Lovecraftian tale that introduced the Order of the Shining Trapezohedron among its protagonists, LaVey formed the Order of the Trapezoid within the Church of Satan." Also, q.v. this .pdf of _The Satanic Rituals,_ which includes a chapter called "The Metaphysics of Lovecraft," featuring two rituals, "Ceremony of the Angles," and "The Call to Cthulhu" (both penned by Sir Michael A. Aquino, Ph.D., GME). In related context, there is also "The Commentary on the Seal of the Nine Angles," by Aquino, as well)
Oh, and not to confuse the issue any further (apparently, those angles can be disorienting, even to those who follow the Left Hand Path); but i should correct the above references to note that, according to MathWorld @ Wolfram Research, "the name for (the Trapezohedron) is not particular(ly) well chosen since their faces are not trapezoids." I'm sure that it all adds up if one uses the proper qlippothic gematria (one could also inquire of the The Nephandi).
And if you really want to know for certain how many sides there are to my lemming (as if you hadn't guessed by now)?
Take the quiz at dicepool.com