Following the way that flags are constructed, the most important distinguishing feature of a banner is that it is cut up into cut by lines. This is so straightforward that it is somewhat difficult to discuss, but there are some strict definitions of what counts as a line, and how they interact with points.

1. A line can be constructed by following all the rules of straightedge and compass construction, in addition to any of the following new rules provided.
2. Some points have been already defined in order for the construction to begin. A defined point is:-
   • One of the seventeen pre-defined points, sixteen around the perimeter of the octagon and the centre. See section 2.2.1.1, below.
   • A point defined by the intersection between previously-defined lines.
   • A point defined by moving a previously-defined point along a previously-defined line by some specified distance.
3. A line can be defined from a previously-defined line rotated from a previously-defined point by some arbitrarily specified angle.
4. A line can also be some kind of curve, particularly an ellipse, for which see section 2.2.1.3.

Unlike Euclidean lines, lines on banners may contain a width. It may be a fixed width in units of content units, or it can also be a special width known as “hairline”, written \(h\). A line of width “hairline” means that it is as thin as visibility permits, i.e. its width is large enough to be able to be recognised as a separate region of colour while at the same time minimising such a value. A line with no width is considered a boundary between two regions, whereas a line with a width is a region of colour in and of itself. A line with a hairline width is typically understood to be an analogue of the Earthling flag practice of fimbriation.

Sometimes, instead of defining a line, entire shapes can be added to a flag by first defining it using other methods and then inserting it to the banner. The shape is something like “a regular pentagram” or “a regular heptagon” – a shape that is cumbersome or impossible to define with methods described above but intuitively obvious and then fixed into the banner by specifying enough constraints so that only one qualifying shape and orientation can satisfy it. This is not always guaranteed by a particular specification, so it is vital to keep a reference picture in mind (and in the description) so as to provide a fallback if the description is not sufficiently unambiguous.

Once the banner is cut up by lines and shapes, they bound areas. These can then be filled with colours. This is part of the definition of these words in a flag context, even though in daily life performing these actions would imply these without explicit instruction.

For various reasons, including visibility and æsthetics, areas have a minimum, positive and finite size for every flag. This minimum can at times alter the design of a flag as it can be derived from construction constraints.

As for colours, this is also fairly straightforward, though there are significant differences between ovexes and flags. In particular, ovecs colours are not authoritative – within reason, the colour of any area may vary as long as it satisfies these conditions:

• The colour is available – the maker of the ovecs is able to use it to make the flag. In particular, it means that if a ovecs requires a colour that is not found locally, then the manufacturer can and will substitute it for one that is as long as it is perceived to be similar.
• The colour is close – objectively, this means that it is closer to the target colour than to all other plausible colours. As the years go by, more and more plausible colours are added, but there are also tools to determine whether or not a colour is close enough in an official sense.²
• The colour is flat – the entire area can be coloured with (more or less) the same colour, preventing the usage of dyes that are too expensive to create even if it is technically available. It also disallows gradients and patterning to some extent – though see below for more information.

In modern times the number of target colours is at or around 40 to 50. 32 of them are in a five-dimensional colour space which resembles RGB but with two extra shades, one for the near-infrared and one for the near-ultraviolet, written in this five-number format \((i\; r\; g\; b\; u)\), where each variable may be 0 or 2. The remainder are other colours that are named in some cultures and so must be distinguished, like “warm brown” \(= (2\; 2\; 1\; 0\; 0)\), or “silver” which does not have a representation in this format.

Some flags have designs that come from a design space different from those of ovexes, but for various reasons they have to appear on ovexes. These may be logos, which use geometry that is hard to describe; or they may be from something like heraldry, where complexity and elaboration is not just tolerated but accepted. Describing these systems in native ovecs terms may be outright impossible or it would be too difficult or unenlightening to do so (14|24). And so, devices are invented to solve this issue.

Devices consist of two parts: an anchor point, which is where the device “is” in an ideal sense, and one or more “scaling points”, which are used to calculate the size and orientation of the device.

Devices do not need to obey any rules regarding colour and area, and they may contain arbitrary detail. They are conceptually understood to be only “on” a single point in the graph.

A flag can have multiple devices, and while they can overlap this is not commonly done. It is up to the flag’s designers to figure out how to keep them away from each other by correctly specifying the scaling points.

An included ovecs is a smaller ovecs used in a design of another ovecs. It is equivalent to placing another flag in canton. Unlike with Earth flags however, An included ovecs is placed in the centre, such that the two ovexes’ @C overlap.

By default, the height of an included ovecs is equal to the side length of the ovecs that includes it. That is, if they are both regular octagons, if an included ovecs has a height of \(1\), then the overall ovecs has a height \(1 + \star\). Designers are welcome to change the relative sizes of the flags, however, and also how it is placed within a flag.

Somewhat common in with ovexes but much rarely seen on flags is the inclusion of two or even more ovexes in an ovecs. In this case, due to space considerations, neither ovecs would be able be able to align their centre point to the original ovecs’ @C. In this case, the designer has a lot more freedom on placement.

The area not covered by the included flag is typically in some way “an extension” of it, and the flag is designed around the included flag. One particular use case of an included flag is when a station needs a flag and it wishes to adopt and extend the flag of the area that it serves. In that case, the extension will revolve around the station and its relation to the main flag.

In either case, the included flag is an inclusion, and therefore the flag as a whole is not an extension of the included flag. Therefore, it is not common practice to attempt to integrate the included flag into the main design. Historically this is because the central flag may change due to the patron of the entity – whose flag is represented by inclusion – also changing, and at a relatively rapid clip.

Indeed, included flags are used to indicate some kind of genetic relationship between the entity represented by the whole flag and the entity represented by the included flag, much like how putting a flag in the canton does with Earth flags. This practice has become much rarer in modern times due to the development of many-mounting, which we will discuss in a later chapter, but old flags continue to use this tactic and the semantics are not the same in any case.

In a technical sense, an inclusion is a special sort of device which is another flag. Its identity as a flag is not taken advantage of fully in the description however; it is presumed to be atomic with no inner structure to it other than its dimensions and centre point.

The contents on the flag all have to be in the same relative position to each other. This is accomplished by the usage of landmarks and measurements from those landmarks.

Specifying where such lines are drawn is done by way of an abstract unit of length which has no name but is occasionally referred to as the “content unit”. This unit of length is only good for one banner at a time; a length of 1 on one banner is not necessarily the same as a length of 1 in another banner. Instead, the size of this unit is determined by ensuring that as many relevant quantities as possible receive an integer.

The value \(\sqrt{2}\) is special and is usually indicated by *. This value is considered an integer for the purpose of measuring flags. For instance, the value \(3 + 4\sqrt{2} = 3 + 4\star\) is an “integer” for the purposes of scaling the length unit.

If a banner is a regular octagon and the design is “innumerate”, meaning that it does not need to use the content unit at all, then its side length is length 1 and the size of the banner as a whole \(1 + \star\).

As the size of the content unit is only useful within a flag, another length unit is needed to specify the size of a flag relative to other flags. This is where the “relational unit” comes into play. This length unit is useful amongst groups of flags, and with some care this can be extended to all flags in general.

The relational unit is defined simply by setting the height or width of some reference flag to be equal to some fixed value. As with the content unit within a single flag, this value is scaled in such a way that amongst the entire group, all of them have to be integers, though in this case it is required that the smallest flag should have a minimum value of 12. This reference flag is generally considered to be the most important flag in the group. For example, in a many-mounting situation where many flags are combined together to represent one overall entity, the flag that represents that overall entity would be considered to be the “most important flag”.

For most flags, which are regular octagons, using the height or the width would not result in any difference. For the flags that aren’t however, which one is used is important, and this is done in a case-by-case basis. In general, the longer of the two is selected, but some cultures would require the width or the height specifically.

The relational unit is also used to handle some modifications that are done to a flag outside of the usual flag design rules which we will describe in 3-usage.html#orgb451368.

The content unit is deeply unpredictable in size from flag to flag because of the large freedoms afforded to flag design. In contrast, the relational unit’s size is constrained because the rules of sizing flags relative to each other is comparatively much stricter. Because of this, the size of the relational unit does not commonly vary beyond the minimum size imposed by the previous paragraph.

The relational unit is usually expressed as a bare number, but if it also shows up with the content unit, then it is circled, for example: \Circled{12}.³

For any single flag in the world, there is an equation that describes the relationship between these three unit systems. This equation is usually put somewhere in the plan to create a flag and looks something like this: \(\Circled{12} = 15 = 16\text{ cm}\). This means that 16 centimetres is equal to 15 content units as well as 12 relationship units.

Similarly, if a flag designer wishes to indicate how tall or wide a flag is, he can write \(\Circled{12} = 470 + 470\star\), meaning that the primary dimension of the octagon, be it height or width, is \(470(1 + \sqrt{2})\). In this form, using the value \Circled{12} is customary, and if the octagon does not fit comfortably in a square, then examining the figure should give it the idea as to which dimension is referred to.

A area of light colour can only be bounded by areas of dark colours. Similarly, an area of dark colour can only be bounded by areas of light colours.

There must be a certain value \(\delta a\) for which all areas described within a flag must exceed.

Strictly speaking, this does not apply to areas of colour in a device, as they are considered atomic and can contain an arbitrary figure. This is because devices are typically drawn elsewhere and stuck on. However, in practice, instead we have another quantity \(\delta a_D < \delta a\) which forms the minimum area for device drawings.

The legend must consist of an even number of graphemes. The number of graphemes must not be excessive.

One additional constraint not mentioned is that there something of a soft limit as to the number of graphemes that can be included in the legend. The intention of a legend is to provide a short code to distinguish between things that coïncidentally have the same design, or to quickly create flags for similar objects that share similar symbols.

With the above in mind, a code consisting of too many graphemes would simply consist of entire words, which defeats the point of having a short code to distinguish things. In general, there is a soft cap of 12 graphemes, beyond which the legend becomes a caption which is unsuitable for this purpose.

Of course, how much a grapheme represents depends on the script. This gives the true limit to what can be written into a legend: a maximum of one word, whatever that may mean to the language in question. Using the culture prevalent at the present day, the three alphabetic scripts that are commonly used generally have a culture of abbreviation that makes it so that the graphemes to be chosen are worth approximately one letter in English. These would reference codes that are available in the Tree of Knowledge.

Text in the legend must remain clear even in hostile typography. How the legend is written is largely beyond the control of the flag designer; the flagmen are given significant latitude to how it is written. In the modern day, the black text, white background and black border is standard primarily because it is the most expedient; however in the past the only requirement is that there is a border and that the text can be distinguished from the background.

Indeed, even in the modern day there are alternate ways to put the legend. Due to the octagonal shape of the banner, there are two crevices that are very receptive of glyphs. This allows for a display of a flag with its legend’s glyphs placed inside those crevices, as is demonstrated in the cover page of this very book.

A good flag is always describable using standard terminology. The best flags avoid devices, or can describe them “longhand”. A flag comes with a description, which is the flag but marked up with red lines that specify (somewhat informally) the proportions and angles of the flag in question. Though informal, the description is in such a way that the flag can be reconstructed even if it is drawn out of scale.

One of the more important implications is that complicated patterns that are beyond the ability of descriptions to handle can be considered to be not æsthetic. These are inevitable, however, due to historical reasons – as mentioned previously they are usually heraldic patterns or have similar provenance where such complexity is tolerated, accepted, or even celebrated. Thus, when these figures eventually make it onto flags, they are allowed in as elementary objects (i.e. without further substructure) and called “devices”. Thus, devices are analogous to charges in heraldry.

The presence of devices on a flag is not generally considered remarkable. Instead, if a flag does not have a device, yet still remains highly recognisable, then it is considered to be a “great flag”. One particular exception, given in the headline above, is that if a sufficiently simple device can be described “longhand”, i.e. using the normal description language to construct the device without reference to outside information, then its status as a device can be ignored. This sort of device is generally not particularly complex, and the requirement of being describable generally gives it a complexity ceiling and a certain æsthetic that all “good flags” end up converging on.

Even though devices continued to be used even in respectable flags, this restriction ends up influencing flag design in other ways. Over the years, flags tend to dispense with highly complicated figures included as devices, especially those related to natural objects like animals and plants. In their place are either stylised depictions of their more salient features, or their comparatively simpler-to-draw products. Even artificial objects tend to be simplified somewhat for the sake of easy specification.

This simplification also created a class of devices that are highly describable. Such “standard devices” typically have a general meaning, and are orientation-dependent. One such standard device is a particular quadrilateral defined as in figure 4, called “the tree”. It represents, amongst other things, motion, strength, and as its name suggests, trees and nature. However, rotating it by 180° would turn it into another device called “the club” which has separate meanings, and if it faces diagonally it would have yet other meanings. With the sharp point facing down, it is “the shovel”; and with the sharp point facing up, it is “the sword”.

Other “standard devices” include the pen, representing writing and journalism; and the lines, which represents text, books and literacy.

An analogue to the general prohibition on text on Earth flags is that they are considered not describable on ovecs, and as graphemes are generally fairly complex for what information they encode including them on the banner imposes a large penalty in being describable. However, such a rule is generally unnecessary as legends provide an obvious and effective outlet for anyone wishing to provide text that would otherwise appear on a banner.

A good flag can be recognised even without colour. Although colour vision is generally excellent for kilis, uncontrollable lighting conditions and difficulties in securing colour resources in historical eras make it so that being able to remain consistent in a specific shade is generally impossible. For this reason, the number of colours that are permissible in a flag is generally quite small compared to other things, though still much higher than on Earth flags.

Nevertheless, the best flags can be recognised even in “outline” form. The “outline” form of a flag is simply the flag but with lines drawn between areas of constant colour, as well as outlining devices which may or may not have their own rules regarding how it is outlined. However, strips of colour inserted as fimbriation are disregarded and is counted as the line drawn between areas of constant colour.

This principle generally discourages basic colour pinwheels, which is analogous to colour bands or tricolours on Earth flags. (38|54) Along with the principle of description, there is both a complexity floor and ceiling when it comes to ovecs design, which is the basis for ovecs æsthetics.

Some flags do not have colour information at all, and only exist in outline form. These are called “colourless flags” and their æsthetic value is somewhat complicated. On the one hand, their colourlessness is considered highly æsthetic; on the other hand, there is the distinctiveness ceiling is lowered by removing a dimension from design. They are thus sometimes considered a separate thing from ovexes, which is also appropriate as colourless flags appear more often in print media and letterheads.

If they do appear as a physical ovecs outdoors, their colours are decided similarly to that of legends; in modern times, the colours are fixed with the outline being in some shade of dark blue and the background being white with an optional black border for the banner; in the past, and in certain other contexts, colours are determined by external concerns such as availability of materials.

The best flags do not rely on distance measurements. When placing features on a flag, there are some ways that one can specify it, using the methods outlined in section 2.2.1.

Some of these rules require a distance to be given. The unit of distance is entirely arbitrary and differs from ovecs to ovecs, relative to only the smallest feature on the flag that requires description, which makes it somewhat arbitrary and otherwise not pretty. Thus, it would be much nicer if one can avoid using them altogether when describing the flag.