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Adrakhonic Theorem

Proof of the Adrakhonic Theorem as seen on the hull of the Geometer's ship the Daban Urnud

The Daban Urnud ("Second Urnud") is a habitat ship with some 40,000 occupants which travels from a different Cosmos to Arbre. Originally built on Urnud during a world war, it was meant to act as an interstellar colonization ship, headed for a star just 1/4 light year away. Instead, it discovered a means to travel to an alternate cosmos by accident, but now does so deliberately.

Prior to arrival at Arbre, the DU has visited three different worlds other than Urnud. Each world has a different physics, but is otherwise quite similar. The worlds visited were Tro, Earth and Fthos. At each world, there is a first contact scenario known as Advent which tends to cause considerable chaos on the visited world. After the chaos, natives of the visited world have ended up reconstructing the ship and contributing colonists for the next trip.

When the DU arrives at Arbre, it does so without contacting the people. However, it is eventually discovered both by Fraa Orolo and others. Because of its shape and design, those on Arbre refer to it as the "Icosahedron" or "Hedron."

The DU has a diagram on one of its faces, displaying a proof of the Adrakhonic Theorem. This diagram led people on Arbre to name the occupants of the DU the "Geometers." The ship also has images of the four planets of its inhabitants on the outside.

During the Advent at Arbre, a team of Avout attack the ship, disabling its Worldburner weapon in the Battle of the Daban Urnud.


The ship visited Earth in approximately 2028. Jules Verne Durand said the ship visited Earth 50 years after the death of Kurt Gödel, who died in 1978.

Internal Politics[]

The Ship[]

The ship consists of 16 spherical habitats, known as Orbs, contained within an icosahedron. The Orbs are in 4 groups of 4, and spin around the center to generate synthetic gravity. Each orb is half-filled with water, and the inhabitants live and farm on ships floating on the water.

At the base of the icosahedron is a heavy duty "pusher plate." This plate is connected to the rest of the ship via strong shock absorbers. The ship moves in normal space by detonating nuclear explosives on the other side of the pusher plate. The blast pushes the plate and the momentum is transferred to the ship via the shock absorbers.

Each face of the icosahedron consists of crushed gravel bound into a flat plane, to provide protection from meteoroids and the radiation of space. At the vertices are various command and observation stations, including one for the WorldBurner which is attached on the outside.

The Orbs are connected by tubes to a central column. At junctions, there are ball valves which can be opened to allow free traffic, or closed to seal off air.

Each cosmic group within the ship has 4 Orbs in a staggered column (staggered due to the 45 degree rotation between consecutive groups of four Orbs). The lowest numbered Orb for the residents of a given cosmos is the higher-status Orb where leaders live. The highest numbered Orb is the least important. They're also numbered in order in which the various cosmi were visited by the DU. So top ranking Urnudans live in Orb 1, lowest ranking ones in 4, Troans in 5-8, Laterrans in 9-12, and Fthosians in 13-16. In each Orb, the air, water and other elements of the native planet are kept. The shared columns and facilities contain a mix of all 4 forms of air. Residents entering the shared areas or other Orbs must be acclimatized to the less efficient use their blood makes of this air.

In an emergency the ship can pivot to put the pusher plate between it and danger, however, this causes considerable disruption due to the water in the Orbs.