Click on entry for graphic              Underline = glossary entry

asymmetric motivation - intrinsic dynamism of the cubodal wheel, most starkly depicted by its edge-on

            left/right asymmetry where squares (or triangles) on one side match their counterparts on the other

            side only by way of rotation.

bicycle - 2-wheeled individual land transporter; in conjunction with human propulsion, the moving system of

            highest energy efficiency in terms of weight moved, distance traveled, and energy consumed; the

            mobility artifact most easily derived from the transport template. 

celestial cube - either of the pair of co-cubes appended to the earth-centered cuboda’s equatorial squares

            whose parallelism unifies the cubes' patterns. In practice, the prime cube always projects from an

            equatorial position; while the co-cube projects to a specified latitude upon secondary rotation.

co-spinning wheel formula  -  Sn = D(√3N -1) where S is the separation between co-spinning (alternate)

            circles of a hexagonal array; D is circle diameter; and N the number of circularly-nested layers of

            separation between such circles.

cuboctahedron - a polyhedron featuring 24 identical edges common to 6 squares adjoining 8 equilateral

            triangles that alternatively converge on 12 identical

cuboda -  the cuboctahedron; for qualifying purposes, the

            adjective is "cubodal"

cubodal angles - 7 angles made by symmetrically sloping

            squares, triangles, and edges of the 4 prime cubodal

            orientations - 30˚, 45˚, and 60˚ are exact angles; while 20˚,

            35˚, 55˚, and 70° are approximate. 35˚, 45˚, and 55° each

            occur twice.

cubodal shell - the earth-centered cuboda minus its 12 outer

            spheres, as well as the internal lines radiating to their

            center-points, with the exception of the 2 required to

            orient the shell coaxially with the central earth sphere

cubodal wheel - the cubodal orientation viewed in profile in which the hexagonal plane faced bisects the

            spheres that formed to in turn form circles patterned with the bisecting lattice; its axis of rotation

            passing through the oppositely oriented triangles on either side of the hexagon.

deep nesting - sphere placement into a vacancy formed by either

            a triangular or square cluster of spheres.

diamond grid - alternate grid derived from the earth-centered cuboda’s skewed “diamond” squares. In any

            given immediate locality, this grid is directed northeast to southwest and southeast to northwest.

disc orientation - the cubodal wheel oriented such that its central hexagonal plane parallels the surface

            of intended travel or operation

edge differential -  from a geocentric cubodal perspective facing a vertically-aligned triangle, the angular

            difference between its (30°) sloping edge in that position and the position rotated to in which that edge

            is directly faced and sloping at 31.5°. The 1.5° difference is keyed to various forms in flat contouring

equatorial axis - an imaginary axis set symmetrically through the cubodal shell's opposing equatorial features

            (vertices, square, triangles, or edges) to enable latitudinal location of cubodal lattice orientations via

            secondary rotations.

fusion formula -   ɸ = sin-1 [(√3/3) tanϴ] where ϴ is the angle of a sloping plane (e.g. roof), and ɸ is the

            angle that a matched pair of equilateral triangles of the hexagonally shifted cuboda spread to fit that

            plane - and such that their common joining edge maintains a

geocentric cuboda - the earth-centered cuboda. The

            cuboctahedron aligned coaxially to earth by reason of its

            opposing paired radial lines transfixing its intrinsic central

            sphere.

grid juncture - the point of intersection between grid lines

            matched by a mundane pole of the geocentric cuboda.

            Signals a 90˚ intra-grid turn or a 135˚ inter-grid turn

            between lines.

hexagonal expansion - rectilinearly transverse extension of the

            hexagonally-shifted cubodal wheel’s central, vertically-

            oriented hexagonal lattice, comprised of unit triangular

            prisms.

hexagonal extension - arbitrary hexagonal expansion from the

            hexagonal lattice of the cuboda wheel; capped by a

            cubodal lattice of shifted orientation.

hexagonal shift - a relative 60° shift of a cubodal wheel half -

            resulting from the cuboda's bisection along its central hexagon; when halves are rejoined, planar

            types adjoin along the central hexagon (instead of alternating) to form a symmetry mirrored on either

            side of that hexagon.

inherent angles - angles associated with an angle explicitly employed in a topographic construct from a

            particular a cubodal orientation.

lattice - a repeating 2 or 3-dimensional pattern. The 3D cubodal lattice has tetrahedra and octahedra

            components; the cubical lattice has one component - the cube. The 2D rectilinear lattice has square

            components; and the hexagonal lattice has triangles - oriented in 2 ways.

mundane pole - In the context of the earth-centered cuboda, any of the 8 vertices not of the polar and

            equatorial vertex-pairs. The 8 are indistinguishable from each other, each constituting a juncture

            between orthogonally oriented triangles and the 2 basic square orientations.

octahedron - A regular polyhedron comprised of 12 edges joining 6 points that define 8 triangles encasing

            3 squares.

orthogonal - at a right angle to; 90° in relation to; or perpendicular to a line or plane

path - grid lines (P-R or diamond) expressed 3-dimensionally with the (20°, 35°) angles associated with the

            cubodal wheel to in effect mirror wheel geometry, and

planar nesting - in rational accretion, nesting a sphere between

            2 contacting spheres to form a plane, or to extend an

            existing triangular plane.

polar-rotational (P-R) grid - the prime grid coinciding with lines of

            longitude and latitude, i.e., true north, south, east, and

            west.

polyhedron -  a 3-dimensional form comprised of polygonal faces

            such as squares, equilateral triangles, etc. Of these,

            GDCode employs the cuboctahedron, the tetrahedron, the

            octahedron, the hexahedron (cube), and the triangular

            prism.

primary rotation - rotation of the cubodal shell coaxially aligned to earth. Speed of rotation is indeterminate,

            such that cubodal features may be positioned directly above the equator at any longitude, at any time.

quarter wave - the smallest natural division of a trigonometric wave - from trough or crest to the next point

            of maximum slope. Useful in tower, landscaping, nose cone, etc. design

rational accretion - a deliberative 2-phase process of placing equal-sized spheres according to an emerging

            pattern that addresses how the cuboda and cube might be arrived at from basic entities and principles.

secondary rotation - rotation of cubodal squares, triangles, or edges, or vertices about any of 4 imaginary

            equatorial axes for the purpose of instantaneous latitudinal positioning. Follows primary rotation.

tetrahedron - The simplest polyhedral form, comprised of 4 equilateral triangles meeting along 6 common

            edges that join 4 points.

transport template - the 3-dimensional pattern of the hexagonally-shifted (and transversely expanded)

            cubodal wheel, with the central plane oriented vertically and elongated in the direction of travel.

triangular prism - a polyhedron composed of 3 triangularly arranged squares meeting edge to edge.

            The basic geometric unit of the transport template's hexagonal expansion.

universal link - a linking intermediary able to directly link one of the 4 prime cubodal orientations to another.

            A cube link may serve in this capacity externally, while internally a sphere may be a universal link.

vertical wave - a wave form whose periodic curve is bounded by points having 90˚ tangents, and

            characterized points of minimum slope halfway between those bounds.

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