The development of the cardboard box with 13 surfaces


In the mathematical field of topology, a development is a countable collection of open covers of a topological space that satisfies certain separation axioms.

Vickery's theorem implies that a topological space is a Moore space if and only if it is regular and developable.

Cardboard box

Cardboard boxes are industrially prefabricated boxes, primarily used for packaging goods and materials and can also be recycled. Specialists in industry seldom use the term cardboard because it does not denote a specific material.
The term cardboard may refer to a variety of heavy paper-like materials, including, card stock, corrugated fiberboard, or paperboard. The meaning of the term may depend on the locale, contents, construction, and personal choice.


13 (thirteen) is the natural number following 12 and preceding 14.
Strikingly folkloric aspects of the number 13 have been noted in various cultures around the world: one theory is that this is due to the cultures employing lunar-solar calendars (there are approximately 12.41 lunations per solar year, and hence 12 "true months" plus a smaller, and often portentous, thirteenth month). This can be witnessed, for example, in the "Twelve Days of Christmas" of Western European tradition.


A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is the portion with which other materials first interact. The surface of an object is more than "a mere geometric solid", but is "filled with, spread over by, or suffused with perceivable qualities such as color and warmth".
The concept of surface has been abstracted and formalized in mathematics, specifically in geometry. Depending on the properties on which the emphasis is given, there are several non equivalent such formalizations, that are all called surface, sometimes with some qualifier, such as algebraic surface, smooth surface or fractal surface.
The concept of surface and its mathematical abstraction are both widely used in physics, engineering, computer graphics, and many other disciplines, primarily in representing the surfaces of physical objects. For example, in analyzing the aerodynamic properties of an airplane, the central consideration is the flow of air along its surface. The concept also raises certain philosophical questions—for example, how thick is the layer of atoms or molecules that can be considered part of the surface of an object (i.e., where does the "surface" end and the "interior" begin), and do objects really have a surface at all if, at the subatomic level, they never actually come in contact with other objects.