Overhead, a lone albatross glides effortlessly through the clear sky, uncomprehending of the curious sight on the ocean's surface. An awkward tetrahedron cuts through the waves, balanced precariously by some miracle of geometry. A triangular sail catches what little wind can be found and drives the small ship forward cautiously. On the ship's deck are three figures in varying states of anxiety and sickness. The first leans nervously against the mast, the second by the entryway to the ship's interior, and the third stands by the front of the ship, staring blankly into an infinite expanse of ocean.
It has been several minutes since any of the crew has spoken, and hours since any meaningful conversation. An implicit understanding of their errand's improbable logistics leaves them without much to say aside from brooding and regret.
A muffled retching sound from the deck below breaks the silence.
"Could you at least do that overboard," calls the one by the door, weary and irritated. There is only groaning and incomprehensible muttering in response, not that he is listening for it anyway. Silence once again returns, bitterness hanging in the air.
The figure by the mast sighs. "Bernhard, stop scowling. Your bitterness is even more unbearable than their seasickness." She pronounces the name deliberately, as what was once only a transient appellation for a future citizen (to be christened again with the proper numerical name) has suddenly become permanent for these exiles.
Without relieving his grimacing countenance in the slightest, Bernhard turns and speaks coldly in return. "I have reason to be bitter, Sophie. But sickness does not justify that kind of pitiful whining." By this time, the sounds from the cabin have largely subsided, but for the occasional whimper. "Being locked in there is only worsening it anyway, so they have only themselves to blame."
"Did you not send them down there, though, so you would not have to hear it?"
"It was the least odious option. I would still prefer silence," he responds with a pointed glare. Their captain, for lack of a better word, turns from his post and nods meaningfully, waiting for the other two to turn away from each other before gazing again at the horizon. It is not the first time today a conversation has ended so abruptly.
A geometer's compass extends its spindly legs across the network of intersecting lines, tracking a path from a conspicuously triangular island to another larger, mass of land. The map is a meticulous copy of the original taken from Tritopea's foreign visitors, with Tritopea itself a tiny triangular speck. Lines of latitude and longitude have been replaced by the Tritopean three-parameter coordinates, forming a lattice of equilateral triangles. Leonhard, once poised to join the hallowed ranks of Tritopean mathematicians, is now reduced to applying his craft in a rudimentary, if useful manner.
He scribbles a few calculations on an adjacent piece of paper, and finding them satisfactory, leaves a relatively comfortable cabin for the ship's deck. "I have good news for you, Karl." Leonhard begins without waiting for Karl (still gazing into the horizon) to turn around. "I believe we are on course, and if all goes well, will arrive on foreign shores within a week."
"A week?" Karl turns, with a concerned look. "Then we can only hope there is no inclement weather. I doubt that either us or our ship could survive for that long. Is that all?"
"Yes. We are at least headed in the right direction." Leonhard looks around nervously, feeble optimism deflating quickly. He ducks into the cabin again without another word.
Night serves as both a navigational blessing (though that they are on the correct path is little consolation) and a cause for concern. No one has any desire to sleep with the sickening undulations of their boat, but they have little choice. It is an uncomfortable time for the makeshift Tritopean crew, and an ominous formation of clouds nearing their position (which appears fixed without appropriate point of reference in the sea) does nothing to allay their fears. Dimly wavering lanterns and opaquely screened moonlight through the clouds serve as poor sources of light for Karl, now the sole member to remain on deck. He paces worriedly as the five others attempt to sleep. As droplets of water spray across his face, Karl flinches, hoping it is not the beginning of rain - just foam ejected as his boat pushes through the waves. Do they grow larger, more aggressive, or is it a figment of his limited imagination?