Ancient Roman Icosahedron Dice

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billd89
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Ancient Roman Icosahedron Dice

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lpetrich
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Re: Ancient Roman Icosahedron Dice

Post by lpetrich »

Dice have been around for millennia, and History of Dice – Awesome Dice shows some examples of them.

The oldest known dice are d6 cubes and d4 tetrahedra, and from Ptolemaic Egypt are the oldest known d20 icosahedron and d12 rhombic dodecahedron. The latter one can be constructed by taking a regular tetrahedron, then going vertex - face center - vertex - face center around each edge, with the face center's distances adjusted to make the new faces flat.

Nearly a century and a half ago, d8 octahedral dice were introduced, and over the last half-century, a variety of shapes of dice have been used - Alea Kybos' Dice Collection - covering the full range of Isohedral figure - Wikipedia and also barrel shapes.

So are there any premodern dice other than d4, d6, d12, or d20?
Last edited by lpetrich on Thu Jul 14, 2022 1:45 pm, edited 2 times in total.
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lpetrich
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Re: Ancient Roman Icosahedron Dice

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The math of dice shapes I find interesting.

The axially-symmetric ones:
  • Dipyramid or bipyramid: two pyramids attached at their bases. A regular octahedron is a 4-dipyramid. d(2n)
  • Trapezohedron: quad faces with a zigzagging equator. A cube is a 3-trapezohedron. For base-10 digits, 5-trapezohedra are often used. d(2n)
  • Prism: quad equatorial faces. A cube is a 4-prism. d(n,2)
  • Antiprism: alternating-direction triangular equatorial faces. A tetrahedron is a 2-antiprism and an octahedron a 3-one. d(2n,2)
The polar faces of the last two are either ignored or made unusable. One way is with pyramidal caps on them, and an icosahedron is a pyramid-cap 5-antiprism.

The quasi-spherical or Platonic-based ones (Catalan solids):
  • Platonic solids: d4, d6, d8, d12, d20
  • Pyramidal cap on each face: d12, d24 (two), d60 (two)
  • Peak-to-edge splits of previous one's faces: d24, d48, d120
  • Rhombic: d6 (cube), d12, d30
  • Deltoidal (kite-shaped): d12 (rhombic), d24, d60
  • Pentagonal: d12 (dodecahedron), d24, d60
Alex Kybos lists every quasi-spherical one and numerous axial ones.
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lpetrich
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Re: Ancient Roman Icosahedron Dice

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Let's look at the history of their discovery.

The Platonic solids: "They are named for the ancient Greek philosopher Plato who hypothesized in one of his dialogues, the Timaeus, that the classical elements were made of these regular solids." Platonic solid - Wikipedia

Cubical dice go back to at least 2000 BCE in Egypt, and tetrahedral dice to 2600 BCE in Mesopotamia. Royal Game of Ur

I can't find much about the early history of recognition of the octahedron and icosahedron, but from Regular dodecahedron I found this tidbit:
Iamblichus states that Hippasus, a Pythagorean, perished in the sea, because he boasted that he first divulged "the sphere with the twelve pentagons."
Hippasus lived ~530 BCE to ~450 BCE, and Plato wrote Timaeus (dialogue) - Wikipedia around 360 BCE.

Related to the Catalan solids: Archimedean solid - Wikipedia described by Archimedes - Wikipedia (~287 BCE to ~212 BCE). However, the Catalan solid - Wikipedia were described much more recently, by Eugène Charles Catalan - Wikipedia (1814 - 1894 CE) though a rhombic-dodecahedral die goes back to Ptolemaic Egypt.
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