Polyhedral Pantheons: Alternate Polyhedrons

This morning, for whatever reason, I was thinking about using other polyhedrons in the Polyhedral Pantheon methodology.

I originally considered the Platonic solids, partly because they would give the most consistent results, but mostly because the entire idea was prompted by the Rose of the Prophet series written by Margaret Weis and Tracy Hickman.

Platonic Solids

The icosahedron and the dodecahedron (d20 and d12) work well and are trivially transformed one to the other.  The icosahedron has twenty faces and twelve nodes; nodes have five adjacent faces and faces have three adjacent nodes.  The dodecahedron has twelve faces and twenty nodes; nodes have three adjacent faces and faces have five adjacent nodes. According to the methodology, this results in up to thirty-two gods, twelve with six domains and twenty with four domains.  Each domain used will be available to four or six gods out of the total.  This configuration can make it possible to have all nine alignments supported on a single polyhedron.

The octahedron and hexahedron (d8 and d6) are similarly easily transformed one to the other.  The octahedron has eight faces and six nodes; nodes have four adjacent faces and faces have three adjacent nodes.  The hexahedron has six faces and eight nodes; nodes have three adjacent faces and faces have four adjacent nodes.  This results in up to fourteen gods, six with five domains and eight with four domains. Each domain used will be available to four or five gods out of the total.  This configuration does not allow all nine alignments to be supported on a single polyhedron.

The tetrahedron (d4) is transformable to… another tetrahedron.  Four faces, four nodes, each node with three adjacent faces and each face with four adjacent nodes.  This gives us eight gods, each with four domains. Each domain used will be available to four gods out of the total.  This configuration does not allow all nine alignments to be supported.

That covers the Platonic solids.

Non-Platonic Solids

I don’t even have a proper name for the last die most of us have available, the d10.  It’s not a Platonic solid, and for my purposes it has some relatively odd properties:

  • ten faces, each with four adjacent nodes;
  • two nodes with five adjacent faces;
  • ten nodes each with three adjacent faces.

Each d10 thus gives me up to twenty-two gods, two with six domains, ten with five domains, and ten with four domains.  Two of the domains used will be available to six gods, ten domains will be available to five gods, and ten domains will be available to four gods.  This configuration does not allow all nine alignments to be supported on a single polyhedron.

Combining Polyhedrons

It may be interesting, however, to consider what happens if you combine polyhedrons.  I realized that with 2d10 I have, effectively, space for forty-four domain assignments.  If I put, say, Law at the point of one of the d10 and Good and Evil on two of the ‘equatorial’ nodes, and similarly with Chaos, Good, and Evil on the other polyhedron, I end up with:

  • Six gods with the Law domain;
  • Six gods with the Chaos domain;
  • Eight gods with the Good domain;
  • Eight gods with the Evil domain.

Depending on precisely which equatorial nodes I use I will have one or two LG and LE gods, one or two CG and CE gods.  If I try for the most even distribution, I end up with

  • Two Lawful Neutral gods;
  • Two Lawful Good gods;
  • Two Lawful Evil gods;
  • Two Chaotic Neutral gods;
  • Two Chaotic Good gods;
  • Two Chaotic Evil gods;
  • Four Neutral Good gods;
  • Four Neutral Evil gods;
  • Twenty-four True Neutral gods.

That’s a lot of True Neutral gods (though still less, proportionally, than if I try to get all nine alignments on the d20/d12 version).  If I put Law and Chaos on ‘both points’ of both d10 I get something a little broader.

  • Five Lawful Neutral gods;
  • Five Chaotic Neutral gods;
  • Four Neutral Good gods;
  • Four Neutral Evil gods;
  • Three Lawful Good gods;
  • Three Lawful Evil gods;
  • Three Chaotic Good gods;
  • Three Chaotic Evil gods;
  • Twelve True Neutral gods.

This might be more equitable, alignment-wise.

These are simple configurations.  I can imagine funkier configurations where the alignment frequencies are more scattered, but I don’t have time right now to explore them.

Still, I find the possibilities here intriguing.  The d20/d12 model is functional, but this offers more variety.  I’ll have to try it when I get home tonight.

1 Comment to "Polyhedral Pantheons: Alternate Polyhedrons"

  1. December 25, 2012 - 5:57 am | Permalink

    A d10 is a trapezohedron. The d20 and d12 are duals of each other, likewise for the d8 and d6. The d4 is self-dual.

    EDIT: forgot to say: the d10 trapezohedron is dual to a pentagonal antiprism. I don’t know if you can make use of this fact to do any clever correlation between a d10-based and a d12-based pantheon.

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