Nox-Minima: 3D Paper Dome for Astronomy

• Nox-Minima is a 3D paper dome that uses precise astronomical data and tangent plane projections to represent the local sky.
• Its design improves astronomy education by preserving spatial relationships and reducing distortions found in flat star maps.
• The assembly process involves cutting, folding, and gluing precomputed segments, making it effective for classroom and inclusive outreach.

Nox-Minima is a low-cost, three-dimensional paper dome designed as an alternative to flat star maps for astronomy education. Generated from precise astronomical data, it provides accurate local sky views for any chosen date, time, and observing location, while presenting the visible sky as a small, nearly hemispherical dome viewed from the inside rather than as a planisphere, screen image, or outward-facing globe. Its stated purpose is pedagogical: to make the celestial sphere, the local horizon-based sky, and the spatial relations among stars, planets, poles, the ecliptic, and constellations more directly apprehensible through a tangible object that can be assembled from ordinary printed paper (Bessa, 28 Aug 2025).

1. Representational concept and distinguishing features

Nox-Minima represents the visible sky as an inward-facing dome whose zenith is physically overhead. The representation is explicitly topocentric, using the observer’s local horizon-based perspective in the alt-azimuth or local horizontal coordinate system. This is the central distinction from flat star maps and planispheres, in which the zenith appears at the center of a printed disk, and from celestial globes, which can suggest that the observer is outside a sphere of stars rather than within an observational celestial sphere (Bessa, 28 Aug 2025).

The paper emphasizes that this geometry preserves relative spatial distances between celestial objects better than flat projections and avoids some of the conceptual distortions of conventional star charts. It also differs from software such as Stellarium by giving a global, tangible view of the whole sky at once rather than a fragmented or screen-bound one. This representational choice is tied directly to naked-eye observational practice: the observer looks “up” at the stars as under the real sky, rather than translating between a flat chart and a three-dimensional environment.

A common misconception is that Nox-Minima is simply a decorative star dome or a paper version of a globe. The paper presents it instead as a horizon-based local sky model whose form is meant to support reasoning about how the sky is actually seen from a particular place and time. Another misconception would be to treat it as equivalent to a digital planetarium. The article’s comparison is narrower and more specific: the dome’s advantage is the simultaneous, embodied view of the whole local sky.

2. Pedagogical rationale and observational uses

The motivation for Nox-Minima is explicitly pedagogical. The paper argues that astronomy teaching often relies on flat charts, planispheres, or software, but that these can create conceptual difficulties when learners try to understand the celestial sphere, the local sky, and the relation among horizon, zenith, poles, ecliptic, and constellations. Nox-Minima is proposed as useful because its physical form corresponds more directly to actual naked-eye sky observation (Bessa, 28 Aug 2025).

The educational functions described are specific. The dome is intended to support understanding of the celestial sphere as a three-dimensional observational framework; relating the sky to the local horizon and the cardinal directions; perceiving the height of the ecliptic above the horizon and zenith; visualizing the celestial pole and its relation to the observer’s latitude; seeing the relative placement of constellations across the whole sky; and practicing star-hopping and orienting oneself before field observation. It is also presented as useful when outdoor observing is impossible, including periods of unsuitable weather.

The paper further frames assembly itself as part of the educational experience. Cutting, folding, and gluing are linked to fine motor skills and geometric reasoning, and the finished dome can then be used for annotating the movement of the Moon and planets, meteor showers, ISS transits, variable stars, telescope targets, and other events. Additional uses include exploring spherical geometry, tangent planes, basis directions, area estimation of flat regions, and the impossibility of flattening a surface with non-zero Gaussian curvature.

The article also includes an inclusive astronomy dimension. It states that the dome can be adapted for blind or visually impaired students by using relief materials such as beads, sand, raised-ink pens, and thread. This suggests that Nox-Minima is not restricted to visual instruction alone, but the paper does not provide a quantitative accessibility evaluation.

3. Astronomical data sources and construction workflow

Nox-Minima is generated from precise astronomical data, with computations performed using the Python library SkyField and the Hipparcos catalog as the main stellar source. Hipparcos is described as providing position, parallax, and proper motion for about 120,000 stars. SkyField is used to obtain or derive positions and magnitudes of stars, Solar System bodies, constellation lines and names, the ecliptic, celestial poles, and the Moon’s phase and orientation (Bessa, 28 Aug 2025).

The construction workflow begins with the computation of star and planet positions for the selected place and time. The dome is then restricted to the relevant hemisphere of the local sky, excluding projections of points in the opposite hemisphere of a region, corresponding to stars below the horizon. The assembled model is therefore tied to a chosen observing location and date rather than to a generic celestial reference frame.

Because a sphere cannot be unfolded exactly onto flat paper, the hemisphere is approximated by a developable surface made of planar pieces. The hemisphere is partitioned into 72 regions: 12 spherical triangles and 60 spherical quadrilaterals. Each spherical region is replaced by a flat surface tangent to the sphere at the midpoint of the corresponding region. Celestial objects are projected region by region using local gnomonic projection, defined verbally in the paper as the intersection of the tangent plane at the center of the nearest region with the extension of the radius through a point on the sphere.

The drawing workflow is also specified. After the 72 local gnomonic projections are performed, each tangent-plane image undergoes a sequence of transformations to obtain Cartesian coordinates $(x,y)$ on the printable page. Stars and planets are drawn as circles with size varying by apparent magnitude. Constellation and auxiliary lines are drawn segment by segment: if both endpoints lie in the same segment, a straight line is drawn; if a line crosses segment boundaries, it is split into portions and each portion is drawn separately. Stars and planets near segment edges are duplicated into adjacent pieces so that symbols are not cut off.

The Moon is inserted using one of 40 NASA lunar images selected by phase angle. Its orientation is approximated from the local inclination of the ecliptic, and the lit side is determined from the direction of minimum angular separation between Moon and Sun along the ecliptic. Final segments are then rotated so that their lowest-altitude sectors, between $0^\circ$ and $15^\circ$, meet at the base and simplify assembly. The print-ready result is a PDF with three pages, each containing four segments.

4. Geometric formulation and mathematical character

The paper presents Nox-Minima as a geometric approximation rather than an exact spherical unfolding. It explicitly states that the sphere has non-zero Gaussian curvature and therefore cannot be unfolded into a plane. The dome consequently uses many local tangent planes to reconstruct approximate hemispherical curvature when the straight projected edges are aligned and glued (Bessa, 28 Aug 2025).

The mathematical notation printed in the article is sparse. The explicitly given expressions and symbols are the Cartesian print-plane coordinates $(x,y)$, the angular width $30^\circ$, the assembly-related sector bounds $0^\circ$ and $15^\circ$, and basis-vector notation $\theta$ and $\phi$. Full celestial-coordinate transformations from right ascension and declination to altitude and azimuth are not written out in the article; the paper states that these are handled computationally through SkyField.

Several geometric facts are stated verbally. Great circles project to straight lines under the gnomonic projection. The boundary between adjacent regions projects to the straight line defined by the intersection of their tangent planes. Aligning and gluing those straight edges reconstructs the approximate hemispherical curvature. These statements define the geometric logic of the object more clearly than any explicit analytic formula in the paper.

This limited formalism is itself noteworthy. The article does not attempt to derive a closed-form celestial-cartographic treatment for the reader; instead, it combines computational astronomy with piecewise geometric approximation. A plausible implication is that the design is intended to remain reproducible and pedagogically tractable without requiring a full exposition of spherical astronomy formulas in the paper itself.

5. Physical format, assembly, scope, and limitations

Nox-Minima is designed to be made from ordinary printed paper. The paper recommends bond paper of $120\ \mathrm{g/m^2}$, or preferably $0^\circ$0 for greater durability, and explicitly notes that glossy or photographic stock is unnecessary. The printed dome uses 3 sheets of A4 or letter paper, with a maximum dome diameter of 24 cm on A4; printing on A3 increases the maximum diameter to 34 cm. The reported current cost is about 0.15 USD per dome when using three sheets of $0^\circ$1 paper (Bessa, 28 Aug 2025).

Assembly proceeds from bottom to top. Pieces are cut along dashed lines and glued at flaps with white glue. The stars face inward, not outward. The final dome consists of three groups of four segments, assembled separately and then joined together, with a printed letter marker indicating joining order between sections. The paper states that when aligned properly, the paper naturally assumes the correct curvature. The design tradeoff is explicit: 72 regions were chosen to balance fidelity to the hemisphere, planar simplicity, structural robustness, and manageable assembly effort.

In scope, the dome can represent local sky views for any chosen date and location; stars, planets, constellation lines and names, the ecliptic, and celestial poles; the Moon with phase and approximate orientation; skies from past epochs, including as far back as 3000 BC for planetary and lunar positions according to the paper; and indigenous or other cultural asterisms. This makes the object both time-specific and geographically specific.

The paper also states several limitations. The dome is an approximation of a hemisphere using flat regions rather than a true continuous spherical surface. Local sky geometry is reconstructed only approximately through planar segmentation. Stars below the horizon are excluded from a region’s projection. The Moon’s orientation is handled approximately, and lunar libration was not considered. Most importantly for technical evaluation, the article does not provide a numerical positional error budget for the printed and assembled dome; it states only that celestial objects occupy altitude and azimuth coordinates very close to their correct positions for the chosen place and date.

6. Workshops, cultural perspectives, and dissemination

The reported evaluation is qualitative rather than quantitative. First workshops were conducted in Brazil with teachers in the Professional Master’s Program in Astronomy at the Universidade Estadual de Feira de Santana (UEFS) in Bahia, with high-school students at Escola Estadual Stoessel de Brito in Maxaranguape, Rio Grande do Norte, and with members of the general public at events at the Federal University of Rio Grande do Norte (UFRN). These activities were coordinated through Marildo Pereira at UEFS and Leonardo Almeida through the UFRN extension project Cometa Nordestino (Bessa, 28 Aug 2025).

The reported outcomes are consistent across these settings. Teachers’ workshop reports emphasized the dome’s opportunities for conceptual discussion. In a one-hour school workshop with pre-assembled domes, students used them to recognize the sky and discuss Greek and indigenous sky stories. In 90-minute public workshops, participants assembled the dome themselves, and assembly became part of the conceptual learning process. Participants reportedly worked in a “relaxed yet focused manner,” expressed pride in the completed dome, and showed interest in its astronomical content. The author recommends reserving about one hour for assembly in workshops with young people or adults, even when working in pairs.

Cultural interpretation is an explicit dimension of the project. The paper states that four Brazilian indigenous asterisms are currently available: the Rhea, the Old Man, the Northern Tapir, and the Deer. These can be added as connecting lines between stars or sky regions. In workshops, stories from both Greek and indigenous mythology were used to interpret the sky visible on the session date. Nox-Minima is therefore presented not only as a positional model of the sky, but also as a support for discussing different ways of seeing and naming it.

Dissemination is open-access. The design is freely available at nox-minima.net/en, and the website maintained by the author offers open access to images of the sky for any chosen location and date. Since the website launch in July 2024, the paper reports more than 800 images generated for dome assembly, over 1,500 site accesses, and users from 35 countries. These figures indicate international interest, though the article explicitly notes that they are not a formal learning assessment. At the time of publication, the full underlying code had not yet been released, but the author states that the current code will eventually be made publicly available through an open repository.