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US 11,033,806 B2Granted
Methods and systems for designing and manufacturing mathematically fair N-sided dice
AssigneeUniversity of Alaska Anchorage
InventorKatherine Rawlins
Life of this patent
Estimating the term…
Abstract
Methods and systems for designing and manufacturing a mathematically fair N-sided die are disclosed. An example method can comprise selecting an irregular polyhedron to serve as a die, and determining a center of mass of the selected irregular polyhedron die. In an aspect, a size of each face of the irregular polyhedron can be selected such that a solid angle subtended by each face from the center of mass of the selected irregular polyhedron can be equal. In an aspect a system comprising an injection molding apparatus can be used to form the die.
Claims18
A system for manufacturing a die comprising:
- a first injection mold comprising a chamber, wherein the chamber comprises:
- an upper point of an enneahedron, formed from three pentagons having tips converging at an upper vertex, wherein the dimensions of the three pentagons are congruent with one another;
- a lower point of the enneahedron, formed from another three pentagons with tips converging at a lower vertex, wherein the other three pentagons are congruent with one another, and wherein the lower point is opposite the upper point;
- each side of the upper point joined with at least one rhombus selected from a set of three rhombi;
- and
- each of the three rhombi joined to a plurality of sides of the three pentagons and a plurality of sides of a second set of three pentagons, wherein the diagonal width of the rhombus sides is n times a maximum rhombus width, and the distance between the upper and lower points of the enneahedron is in times the maximum rhombus width, wherein n and m are a real numbers such that the die, when tossed, will land with substantially equal probability on any side;
- and
- an injection molding apparatus comprising:
- a top opening having dimensions suitable for passing a quantity of solid polymer material into a heating chamber, wherein the heating chamber is coupled to the top opening;
- a heating element coupled to the heating chamber, wherein the heating element causes the quantity of solid polymer material in the heating chamber to become molten polymer material;
- and
- an injection jet coupled to the heating chamber having dimensions suitable for passing a quantity of the molten polymer material through a head of the injection jet and into the chamber.
9 more elements
A method for manufacturing a die comprising:
- selecting a first injection mold comprising a chamber, wherein the chamber comprises:
- an upper point of an enneahedron, formed from three pentagons having tips converging at an upper vertex, wherein the dimensions of the three pentagons are congruent with one another;
- a lower point of the enneahedron, formed from another three pentagons with tips converging at a lower vertex, wherein the other three pentagons are congruent with one another, and wherein the lower point is opposite the upper point;
- each side of the upper point joined with at least one rhombus selected from a set of three rhombi;
- and
- each of the three rhombi joined to a plurality of sides of the three pentagons and a plurality of sides of a second set of three pentagons, wherein the diagonal width of the rhombus sides is n times a maximum rhombus width, and the distance between the upper and lower points of the enneahedron is m times the maximum rhombus width, wherein n and m are a real numbers such that the die, when tossed, will land with substantially equal probability on any side;
- and
- providing, via an injection jet of an injection molding apparatus, a quantity of molten polymer material into the chamber, wherein the molten polymer material passes through the injection jet into the chamber to form the die.
5 more elements
Dependencies are inferred from the claim text.