The Sixth Polyhedron

by Simon Whitechapel

Nec illi, Terra, gravis fueris: non fuit illa tibi.

Martialis Epigrammata V, xxxiv.

All voices in the palace were muted and all feet unshod, for the Princess Anankë, sole surviving child of King Krummdaggolan, lay in the final stages of her slow decline; and with her were fading the last hopes of the kingdom. Day by day the line of fly-shrouded physicians hanging from the palace wall grew in length and volume, and shrines of prophecy for hundreds of leagues around smoked in lifeless ruin: all had returned answer that the Princess’s death was ineluctable, and against them all, in his wrath, the King had sent his bronze-helmed warriors. Then at last, from the Prophetess of the half-fabled southern Isle of Ictammathae, came an answer that did not swell the veins in his ritually tattooed brows:

“An thou findest a sixth polyhedron,
she will live and bear thy kingdom an heir.”

The five known royal polyhedra were cult-objects in the rough-hewn Temple of sun-god Tsammogwer, saved with hybrid polyhedra of lesser worth from the ruin of the city when it had been sacked by the King and his armies thirty years before: the triangle-faced tetrahedron, carved from quartz; the square-faced hexahedron, carved from tourmaline; the triangle-faced octahedron, carved from sapphire; the pentagon-faced dodecahedron, carved from emerald; and the triangle-faced icosahedron, carved from ruby. Cruder imitations of the five in bronze and lead were found in temples of Tsammogwer throughout the kingdom, for the King regarded them as symbols of his victory and even, in his softer moods, took some pleasure in their symmetry and perfection; and the icosahedron, laid thrice in the cot of the Princess during her bouts of childhood illness, was universally credited with preserving her life, if not those of her siblings.

Having visited the Temple to view the polyhedra again and sacrifice three bulls in thanksgiving to Tsammogwer, the King called for his court architect, the ageing slave Rhanomedhodë, saved by chance in the overthrow of the city and last surviving pure-blood of his race, and questioned him anent the Prophetess’s words (which had confirmed Rhanomedhodë’s final reconciliation to his lot: he was seen to have been pleased by them better than any but the King and his wives, so widely had he smiled to hear them). The slave agreed with the King that he must send his armies forth so soon as he were able, for it flew in the face of all intuition that, in a world so vast and varied, no further royal polyhedra lay ready to be discovered, whether above ground, in the cell of some ascetic wizard of the deserts of Ilgaddrem or Yommtevac, or below, in the crystal-rich caverns of Tresgoththunc or Zlantish. Indeed, the slave went on, it seemed reasonable that, with three known royal polyhedra based on the triangle, there should be a further undiscovered three based on the square and a further undiscovered four based on the pentagon, yielding thus a total of twelve, of which a mere five now rested in the Temple of – and here he bowed his slave-shaven head – sun-god Tsammogwer.

The King, who had followed at least the initial stages of Rhanomedhodë’s disquisition, nodded as sagely as he might and issued orders for the assembly and outfitting of his warriors. In a week they were ready; and the King, seated within the palace on his throne of gold and lapis lazuli, also saved from the wreck of the city, raised a final survivor of the wreck, his sceptre of untarnishing iron. From without, after a few moments, he heard the blast of horns conveying the order to his generals; and soon his throne began to shake faintly with the tread of his departing armies. The King lowered his sceptre with a grunt, confident that one day, a month or year hence, his throne would shake again to signal their return with that of which the southern prophetess had spoken.

Nested polygons

© 2004 Simon Whitechapel

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