TimeStar

TimeStar (JPEG 47k): The TimeStar of the Maya is 5 interpenetrating tetrahedra whose vertices lie on the 20 faces of an icosahedron.
According to Jose Arguelles, time is symbolized by a tetrahedron.
The 260-day sacred calendar of the Maya, which consisted of five 52-day cycles is symbolized by five tetrahedra. Five tetrahedra have a total of 20 points. One of the basic numbers of the Mayan calendar is 20.
The Earth's internal geometry and the solar-lunar cycles were represented by the 20 points of the TimeStar (five interpenetrated tetrahedra) and in the sacred cycle of the Maya.
Compare Plato's most complex solid, the icosahedron, which is comprised of 20 faces centered on the points of the five interpenetrated tetrahedra. .
The 12 pentagonal vortexes which lie under each icosahedral vertex are universal energy inflow points on the Earth's surface and the 20 tetra vertices are outflow points from the planet back to the universe, according to Arguelles.

TimeStar(QuickTime Movie 204K) shows the TimeStar spinning on an axis. This view of the TimeStar shows how each of the 5 interpenetrating tetrahedra are oriented in a similar way to the icosahedron and a common vertical axis. Considering the 20 triangular faces of the icosa in this orientation, there are 5 around the axis of spin at the top and 5 around the axis at the bottom with 10 forming an equatorial band in between these groups (5 with apex up & 5 with apex down). Each tetra has 1 vertex at top, 1 at bottom, 1 at apex up face, and 1 at apex down face. The TimeStar relates the minimum equilateral triangular structure to the maximum equilateral triangular structure.

TimeStar_Redux (JPEG 44k): Timestar Redux is another rendering of the TimeStar which better illustrates the relationship between the 5 tetrahedra and icoshedron.
In this model the icosahedral faces are subdivided into LCD right triangles showing that the tetrahedra vertices are congruent with icosahedral face centers. The tetra edge lengths are exactly 5/4 X icosa edge lengths, an interesting ratio all things considered.

Spherical TimeStar

TimeStar_solid (JPEG 18k): shows the TimeStar as a solid. Note how the intersections of the tetrahedral planes form the pentagonal vortex at the center of the image. There are 12 of these on the TimeStar at the same coordinates as the vertices of a circumscribing icosa (See TimeStar_Redux,JPEG)

Quintet_Dodeca(JPEG 49k): The quintet_dodeca is derived from the TimeStar, and is my own innovation as far as I know. Since the pentagonal dodecahedron is the dual of the icosa it follows that the 5 tetrahedra of the TimeStar relate to this polyhedron also which has 20 vertices, 30 edges, and 12 faces as compared to the icosa's 12 vertices, 30 edges, and 20 faces.
Of the five regular Platonic polyhedra, only the tetrahedron, octahedron, and icosahedron are triangulated and therefore considered to be structures in Synergetic Geometry. The cube and the pentagonal dodecahedron, not being triangulated, are unstable.
RBF puts great emphasis on the Duotet Cube (a cube stabilized by 2 inscribed tetrahedra)as the domain of the jitterbug transformation in metaphysical space (Synergetics2). There is little mention of the pentagonal dodecahedron in Synergetics but I think the Quintet Dodeca may have a role to play in Synergetics analogous to the Duotet Cube.

Quintet_Dodeca movie(Quicktime movie 414k):shows the Quintet Dodeca spinning on vertical axis. Gives could perspective on the tetrahedral alignment with the vertices of the dodecahedron.

QD Kite (JPEG 19k): The QD kite was inspired by the TimeStar and my wife and daughter's newfound love of kite flying. I was wondering if any of you aerodynamic experts could tell me if it will fly before I bother to build it. It is already flying in my imagination as a concept that should be employed in Synergetics.

VE in TimeStar Tetra (JPEG 25k): This image shows one tetrahedron positioned inside the pentagonal dodecahedron as it would be (along with 4 others) to form the TimeStar. Inside the tetra, concentrically, are the octahedron and VE (vector equilibrium). This image will help in understanding the one which follows.

The idea for the following image came from Gerald de Jong (see Tensegrity Jitterbug section):
TimeStarVE (JPEG 29k): This is the VE in the above image duplicated and rotated at 72 degree intervals like the tetra would be in the TimeStar. The VEs share great circles.
According to Gerald, "since this represents the combination of five IVM's, and they are also showing some *harmony*, we may indeed be approaching the least common multiple of all the regular polyhedra, and with it the most generalized coordinate system which grabs tets, octas, and icosas!" Stay tuned for further developments as this idea evolves.

The following movie shows the above TimeStarVE spinning on an axis. It is much easier to see the 5-point and 6-point stars which make up the surface of the form.
TimeStarVE spinning (Quicktime movie 147K): Note how the hexagonal planes of the VEs (20 in all) double up and form what Gerald termed as 10 "funky great circles" which are shared by the VE and icosa.

TenseJit_TimeStar movie (Quicktime movie 571K): Integrates Gerald de Jong's Tensegrity Jitterbug with the TimeStar concept.
In the TenseJit_Timestar movie, as the tetra cycles positive/negative(see tensejit_cell.MOV in the Tensegrity Jitterbug section), the cube cell rotates 72 degrees so that the negative tetra is in a new timestar position. As the cube cell continues to rotate on the pent dodeca central axis (axis through the center of 2 opposing pent dodeca faces) the tetra within assumes all of the 5 timestar tetra positions in the first (360 degree) rotation then cycles negative/positive in the next (360 degree) rotation also forming all 5 timestar tetra positions.
The full cycle is 720 degreees and 10 different tetrahedra are formed in the process. These 10 tetra are probably related to the 10 tetra which comprise a full spiral in the tetrahelix.


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