Haloed Bane


The fabric of Sinduin's universe is not atomic, but hedronic (see Plato's Timaeus for interesting parallels). Everything is composed out of 10 elements (olfinis), all but one of which take the shapes of the nine regular polyhedra (zindogaichans lokiter), whose faces/facelets are composed of a number of sub-elementary figures, either triangles or pentagons. We'll call a single elemental polyhedron a hedron (in Horgothic they're called tagekins). Our name for the figures which compose the hedrons is recombinant figures (miminyonobunis); we'll refer to the triangular ones as trianglents and the pentagonal ones as pentagents. The tenth element is a simple sphere lacking in parts.

  • Fire - the tetrahedron
  • Earth - the hexahedron
  • Air - the octahedron
  • Water - the tetrahedron
  • Glace Réelle - the icosahedron
  • Salt - the small stellated dodecahedron
  • Mercury - the great dodecahedron
  • Sulphur - the great stellated dodecahedron
  • Electrum - the great icosahedron
  • Aether - the sphere
9 regular polyhedra

above: the 10 elements, top row left to right: fire, earth, air, water, glace réelle
bottom row: salt, mercury, sulphur, electrum, aether.

Fire, Air and Glace Réelle have equilateral triangles for faces (see picture below, left), each of which is composed of six identical trianglents. They are known collectively as "soft elements." Earth has squares for faces, each of which is composed of four identical trianglents (below, right).


Water has pentagons for faces. A pentagonal face is to be conceived as a smaller pentagon (our pentagent) surrounded by 10 trianglents of 2 different types. The pentagent potentially houses another pentagon and so on and so on.

pentagons and pentragrams

Salt and Sulphur have golden triangles for facelets (below, left), each of which is composed of two dissimilar trianglents. The number and size of the salt and sulphur facelets is exactly the same, but their arrangement is different. Salt and Sulphur are known as the "dark elements." Mercury has golden gnomons for facelets (below, right), each of which is composed of two dissimilar trianglents.

bright and dark trianglents

Each of the facelets of electrum consists of one of two types of sub-elementary figure, both unique to Electrum: the power trianglent (below, left), and Harkuin's trianglent (below, right), which should not be confused with a bright trianglent, although they are very similar.

electrum's trianglents

A brief and probably overwhelming bird's eye view of this physical model goes as follows:

Water, the dodecahedron, is under most interpretative schemes, the matrix and mother of practically All. These words are not meant poetically or philosophically, but literally. The dodecahedron can transform itself in the primary sense into a cube, a tetrahedron or an octahedron. The three latter elements cannot generate each other in this manner, though they undergo intraelemental secondary transformations and interelemental tertiary transformations. These elements, along with Water, can keep transforming in different ways and produce the universe we see around us. In our universe, your Thales would be closest to the truth. What is it about Water's structure that makes it so powerful? The answer is found in geometry. Each of its pentagonal faces is dominated by a pentagram enclosing another pentagon (cf. Euclid Book IV. Propositions 10-11). This mise en abyme, how the watery pentagram encloses a potential pentagon which itself houses another pentagram and so on, is what gives water its great power. The role of the pentagrams is to generate a force within that imparts water its stability and allows it to give birth to other elements (we call this echomagnetism, lodontuli). Birthed by the dodecahedron, the cube still possesses some echomagnetism, though being in every sense of the word less than Water, its faces are more brittle, and thus Earth is quite stable, but quite prone to changing through the breakup of its trianglents (echomagnetism holds the walls of an element together, so that the lower the force, the less stable). Next, Fire and Air are extremely brittle and with very low echomagnetism. Water is very mutable, of course, not through the unwilling breakup of its trianglents, but through the generative force of the pentagrams which replicate its own pentagonic faces and which keep the maternal element in a state of constant self-affirming turbulence. Water does have the tertiary transformative power to shift into the polyhedral faces of Glace Réelle, which can then shift back into water at several level sizes (again, Euclid IV 10-11), as well as quaternary powers that give rise to other elements, and ultimately, the aether.

I will untangle the topics mentioned in the previous paragraph by means of tables, but let me first throw in a couple of comments. First off, the basics of the model resemble Plato's in Timaeus quite closely except that he assigned the icosahedron to water, and left the dodecahedron for the shape of the universe itself. In Belklaun, the dodecahedron belongs to Water and the universe is shaped like an icosahedron. The icosahedron is also the shape of Glace Réelle, and the weirdness of the latter's name is the second thing I'd like to explain.

What I'm calling here in French Glace Réelle is named in Horgothic flanan. Two common nicknames for the element are grond flochi (i.e. true ice) and grond lanan (true mirror). Popular etymology -in agreement with the esotericists, I should point out- has it that flanan is really a conflation of the words for ice and mirror, fl(ochi)+(l)anan. I'm not quite sure if the nicknames reflect this interpretation or if they gave rise to it. The element itself is extremely condensed ice (cf. your Einstein-Bose) and perfectly mirroring, though tending to be extremely dark, the very definition of black in Belklaun (ruka me flanan). Now, in French the word glace in French can mean both “ice” and “mirror”, thus the translation for our purposes.

Then there is the Aether. Just as Water hedrons are the source of echomagnetism, Aether hedrons are the source of gravity. In fact, Aether has no qualities to speak of outside of unity, specific (and ever decreasing) size, and the ability to push (i.e. gravity). It is born of what some have termed the degeneration (tenefama) of Glace Réelle. Glace Réelle has a tendency, when occurring in great numbers, to transform its shape from icosahedron to sphere (that is, it reduces itself into the sphere it always potentially inscribed). The spheres generate force and then gravity ensues, essentially along the lines of LeSage’s theory. Forget about Einstein when it comes to our universe! It should be noted that the degeneration itself is considered the beginning of gravity, or what develops into gravity, just as with echomagnetism the inner tension of Water is both a phenomenon of its own as well as productive of new polyhedral elements. Eventually, all aetheric spheres transform into the dodecahedra they potentially circumscribe. But the process is long and drawn out, and outer space is today full of Aether.

Sub-elementary Figures and their Sizes

There are seven sub-elementary figures, and they come in a reduced number discrete sizes, noted below with Roman numerals. The standard reference for measurements of sub-elementary figures is the mid-sized Water hedron, whose sub-elementary components are defined as being size III. Not all elements contain sub-elementary figures in all their possible sizes.

Soft trianglent
soft trianglent
Fire (24), Air (48)
Glace Réelle (120)
Six Five I (1, √3, 2)
II (√3, 3, 2√3)
III (2, 2√3, 4)
IV (3, 3√3, 6)
V (2√3, 6, 4√3)
Hard trianglent
hard trianglent
Earth (24) Four Six I (1, 1, √2)
II (√2, √2, 2)
III (2, 2, 2√2)
IV (2√2, 2√2, 4)
V (4, 4, 4√2)
VI (4√2, 4√2, 8)
Bright trianglent
bright trianglent
Water (60), Salt (60)
Mercury (60), Sulphur (60)
Five for Water
One for the rest
Five I (Φ, Φ, 1)
II (1, 1, 1+Φ)
III (1+Φ, 1+Φ, 2+Φ)
IV (2+Φ, 2+Φ, 3+2Φ)
V (3+2Φ, 3+2Φ, 5+3Φ)
Dark trianglent
dark trianglent
Water (60), Salt (60)
Mercury (60), Sulphur (60)
Five for Water
One for the rest
Five I (Φ, Φ, Φ2)
II (1, 1, Φ)
III (1+Φ, 1+Φ, 1)
IV (2+Φ, 2+Φ, 1+Φ)
V (3+2Φ, 3+2Φ, 2+Φ)
Water (12) One Five I (Φ2, Φ2, Φ2, Φ2, Φ2)
II (Φ, Φ, Φ, Φ, Φ)
III (1, 1, 1, 1, 1)
IV (1+Φ, 1+Φ, 1+Φ, 1+Φ, 1+Φ)
V (2+Φ, 2+Φ, 2+Φ, 2+Φ, 2+Φ)
Harkuin's trianglent
Harkuin's trianglent
Electrum (60) One One III (2+Φ, [2+Φ][√10/5])
power trianglent
power trianglent
Electrum (120) One One III (3+2Φ, [2+Φ][√10/5],
  • The number in parentheses after each element is the number of sub-elementary figures of said type contained in one hedron of the element.
  • It is vital to understand that for each actual hedron, any figures of the same type that compose it will also be of the same level. Put another way, the number of figures of a particular type on each face of an elemental hedronis fixed (Fire, Air, and Glace Réelle have six soft trianglents for each face, never less and never more, even though on paper we could build up the faces with a different set consisting of differently-size figures).
  • Φ stands for the golden fraction, i.e. the inverse of the golden ratio)
  • The Pelren Academy defines the ali as the length of each side of the smallest water particle in existence. Using your metric system, that comes to a whopping 6.9 nanometers or so. Note that the table above includes measures smaller than an ali, but that they are confined to Water, whose components tend to exist notionally more than actually.

The Aetheric Sphere

Aether comes in spheres, not hedrons. It lacks parts, and does not come in discrete sizes. Instead, each aetheric sphere is born with a specific radius, which in ali is:

$$3 (1+Φ)^2$$

The sphere then progressively shrinks in size until the point where it transforms into Water. That final radius before transfomation, measured once more in ali, is:


Original Hedrons

The quantity of mass in the universe is not constant. Some things are born from nothing, though not spontaneously, but by the presence of certain "sources". Hedrons which can arise without other hedrons as mothers are called original hedrons. Many other hedrons can then be born from transformations (famakins) of these former. Below are the original hedrons, along with their sources.

lifeless and living entities L3 Water It is said the universe is constantly weeping.
lifeless and living entities L1 Earth Is the universe also constantly pooing? (This is why poetry and science ultimately don't mix.)
pre-astral space dust L5 Water PASD refers to any number of elements and compounds which tend to coalesce and form stars (sulphur being key).
pre-astral space dust L5 Fire Meteoric fireballs composed mostly of L5 Fire are a great threat in some systems. Conversely, L5 Fire plays an important role in many planetary systems, and is worshipped by many of our own.
living entities L4 Water Sweat is a classic example.
sapient entities L2 Air L2 Air is born of thoughts. Your scientists might rent their robes (while Descartes rises and takes a bow), but it's not at all crazy. Our theories explain in great detail how the exertion of thinking causes the organic brain to exude air. It is not a case of the non-physical acting on the physical as such.

Table of Elemental Transformations

What follows is a summary table of elemental transformations. 1) The notation "L#" means that the hedron's sub-elementary particles are of size # (thus, an L2 hedron is composed of size II sub-elementary figures). Mercury is an oddity in that each face has two triangles of a different size category (inasmuch as the size standards are determined on the basis of Water hedrons). The convention for mercury is for the size number to indicate the size each dark trianglent. To find out the size of the bright trianglents in mercury, one need simply subtract one from that number. 2) Bidirectional transformations can happen both ways, so that the initial and final hedrons in each row may swap roles. 3) By by-products, loose sub-elementary particles are meant.

1 L3 Water hedron 1 L4 Earth hedron N, N Primary Echomagnetic
1 L3 Water hedron 1 L3 Fire hedron N, N Primary Echomagnetic
1 L3 Water hedron 1 L1 Air hedron N, N Primary Echomagnetic
1 L5 Soft hedron 2 L2 hedrons
of the same element
Y, N Secondary Volumassic
1 L3 Soft hedron 2 L1 hedrons
of the same element
Y, N Secondary Volumassic
1 L6 Earth hedron 2 L4 Earth hedrons Y, N Secondary Volumassic
1 L5 Earth hedron 2 L3 Earth hedrons Y, N Secondary Volumiassic
1 L4 Earth hedron 2 L2 Earth hedrons Y, N Secondary Volumassic
1 L3 Earth hedron 2 L1 Earth hedrons Y, N Secondary Volumassic
1 L6 Earth hedron 1 L4 Air hedron Y, N Tertiary Volumassic
1 L5 Water hedron 1 L4 Glace Réelle hedron Y, N Tertiary Volumassic
1 Fire hedron
of any level
1 Fire hedron
of the same level
Y, N Tertiary Volumassic
1 L5 Salt hedron 11 L4 Mercury hedrons Y, N Tertiary Volumassic
1 L3 Electrum hedron 2 L3 Sulphur hedrons Y, N Tertiary Volumassic
1 L3 Water hedron 1 L3 Dark hedron
and 1 L1 Water hedron
N, N Quaternary Anti-Echomagnetic
1 L4 Water hedron 1 L4 Dark hedron
and 1 L2 Water hedron
N, N Quaternary Anti-Echomagnetic
1 L5 Water hedron 1 L5 Dark hedron
and 1 L3 Water hedron
N, N Quaternary Anti-Echomagnetic
1 L3 Water hedron
and 1 L4 Water hedron
1 L4 Mercury hedron,
1 L1 and 1 L2 Water hedrons
N, Y Quaternary Anti-Echomagnetic
1 L4 Water hedron
and 1 L5 Water hedron
1 L5 Mercury hedron,
1 L2 and 1 L3 Water hedrons
N, Y Quaternary Anti-Echomagnetic
1 L4 Glace Réelle hedron 1 Aether sphere N, N Quinary Gravitational
1 Aether sphere 1 L3 Water hedron N, N Quinary Anti-Gravitational

Here is a table of hedrons actually existing in nature, by element and size. It is not exaggeration to say that, just as Water is the queen of the elements, the L3 Water hedron is empress of the waters. Our universe is unthinkable without L3 Water. Aether is not included in the table because it's not actually hedronic. Its absence does not mean it doesn't exist!

L1 L2 L3 L4 L5 L6

Finally, let's briefly go over each transformation type, with the caveat that the denominations primary, secondary, and so forth are historical and not necessarily scientifically rigorous. The Dolens, for example, have a far more precise classification system in existence, but it simply hasn't taken among us Inculae.

Primary Transformation (Echomagnetic)

Primary transformations all involve L3 Water hedrons transforming into other elements. It is the first transformation type that was well understood and described by our scientists. Strictly speaking, Water transforms into one or another of these elements. However, there is a sense in which one can say that Water that transform into Air first undergoes an Earth stage and then a Fire Stage. Thus, for example, primary transformations into Air take longer than into Fire, which take longer than into Earth.

Secondary Transformation (Volumassic)

The volumassic forces, as the name indicates are linked to the material features of volume and mass and arise as the expression of echomagnetism. Only soft and hard trianglents are affected in secondary transformations, which see these figures breaking up or joining up with others like them through small bursts of volumassic force or pressure. Mixed size hedrons do not exist in nature, though advanced races have gone some way toward creating them in experimental conditions.

Tertiary Transformation (Volumassic)

When volumassic pressures are large, there is a slide or shift in elements, whereby trianglents temporarily lose their features. Note that the tertiary transformations of Fire are notat all trivial, despite the fact that the initial and final hedrons are identical. Fire's unpredictability and lethality largely stem from these events. Both secondary and tertiary transformations are bidirectional.

Quaternary Transformation (Anti-Echomagnetic)

Quaternary transformations are closely connected to primary ones, and take place when the polarity of the echomagnetic forces inside a Water hedron is reversed. The hedrons are stellated, and Salt, Sulphur and Mercury are born as a result. The Mercury transformations are to all living things the most momentous, as they yield loose sub-elementary figures as by-products which serve as conduits for Light as a phenomenon. (It would take me too long to discuss even the basic principles of photology in Belklaun, but the gist of it is that Light is not hedronic, or aetheric, for that matter, but something altogether different that virtually exists -in opposition to Darkness- everywhere, and yet for it to appear in the physical plane it has need of particles that are uncompromised by the crass forces, so that once it is free to reveal itself, it can cover an enormous expanse riding on the merest sub-elementary particle, since once again it is not commensurable with physical size as such, and of course Darkness rides along with it.)

Quinary Transformation (Gravitational, Anti-Gravitational)

In short, Glace Réelle becomes Aether, and Aether becomes Water. This entire tendency or trajectory is called potential gravity (kiomeintal nyekulglari). The first transformation occurs suddenly and very visibly, whereas the second step usually occurs after hundred of years have passed in a process process termed aetheric decay. In that halfway state between the beginning and end of quinary transformation viewed holistically from Glace Réelle to Water, the aetheric spheres decrease in size, and as they do they exert a forward force, which we call actual gravity.

Sustained and affordable space travel is possible once the secret of “safely mass-converting spherical Aether from space into Water at will” is obtained by a species Said Water is useful for advanced travel in two ways: 1) because it is then heated up, producing steam which powers the required engines (otherwise a steam-driven spaceship would need to carry inordinate amounts of Water on board to travel far); 2) because it can, by eliminating gravitational fields around the ship, by this way propel the vessel.

Further Topics in Elementary Physics and Beyond

The reader might wonder how these elements and their components jive with the states of matter (gas, liquid, plasma, solid). For that we'd have to discuss the mathematically much more elaborate theory of kinson, or the specific intensites of sub-elementary figures inside each hedron. Generally speaking, the higher the kinson, the lower the solidity, in order from high to low we get: plasma, gas, liquid, solid, BEC (Bose-Einstein condensate). Fire is usually composed of trianglents with the kinson intensity of plasma, whereas the intensity of the trianglents composing Air is naturally somewhat lower, then Water, and after that Earth and Glace Réelle as the lowest naturally. But of course Water’s kinson can be lowered, thus making it ice, or it can be raised, making it steam. Other elements, like Salt, have more complex kinson patterns. Aether has a kinson of zero.

Beyond the elemental level, there are 39 fundamental compounds who have emergent properties practically as idiosyncratic as the elements'. They are the building blocks of the universe, and they are most stable in configurations of three hedrons: two of the same element (called dominant), and one of a different element (called subservient). The Blood compound, for example, is composed of two hedrons of Water and one of Fire; Terra viva is two-parts Earth and one-part Water, etc.

Another interesting topic intimately associated with physics is magic, which we'll explore in the next page.