Above are the seventeen piece types of sixathi, followed by the seven combos, they were created using Stella4D. We could name the pieces and combos as follows:
Cage of Death - large hollow gold piece - comes from the quit sissid cells, 120 needed.
Ike - large gold icosahedron - comes from the center of the quit sissids, 120 needed.
Gear - large white gear/fan blade shaped piece - comes from the 5-fold sections of gaquatid cells, 1440 needed.
Chopped Log - the other white piece - comes from the two-fold regions of the gaquatid cells, 3600 needed.
Slab - flat but large triangle purple piece near ike - comes from the center of the triangle faces of the srid cells, 2400 needed.
Cap - wide cyan triangle shaped piece near the slab - comes from the center of the triangle faces of the tut cells, 2400 needed.
Pyramid - gold triangle pyramid near the cap - comes from interior of the quit sissids, 2400 needed.
Wall - flat purple piece near the pyramid, shaped like a wide isosceles triangle - comes from the srids, 7200 needed.
Tile - flat cyan piece which is similar to the wall (second largest cyan piece) - comes from the tuts, 7200 needed.
Slate - irregular flat convex purple piece near the tile comes in right and left handed forms - comes from the srid cells, 14400 needed.
Tripoint - small gold concave piece with three points for legs - comes from the 3-fold region of the quit sissids, 2400 needed.
Gem - small cyan piece nearest the tripoint - comes from corners of the tut cells, 7200 needed.
Kitespike - small cyan piece shaped like a kite pyramid, under the tripoint - comes from the tuts, 7200 needed.
Glider - flat concave purple piece between the white pieces - comes from the corners of the srid cells, 7200 needed.
Bip - small gold disphenoid near the chopped log - comes from the quit sissids, 7200 needed.
Counter - long purple piece near the gear - comes from the srids, 7200 needed.
Dit - small irregular wedge shaped cyan piece near the gear, comes in right and left handed forms - comes from the tuts, 14400 needed.
Stellike - composed of one ike, 20 slabs, 20 caps, 20 pyramids, and 60 walls. All folds are inwards except those between the slabs and caps which fold outwards. The result looks like a stellated ike shaped pseudocell when glued together. - gold, purple, and cyan, 120 needed.
Bulb - composed of two tiles and four slates (two right handed and two left handed). Fold inwards and glue the slates together when they meet, it will have a hollow spot inside - purple and cyan, 3600 needed.
Carasel - composed of two gears, ten gliders, ten bips, and ten counters (shhh - don't tell Compadre). The gliders, bips, and gears connect in a way that there are no gaps to glue together. However the counters will need concave tabs between them to glue these together. All folds are inwards except for the ones between the gliders and the bips - white, purple, and gold, 720 needed.
Log - composed of three chopped logs, folded inwards and glued - white, 1200 needed.
Spikup - composed of twelve kitespikes, looks like a mildly spiky cup when folded inwards and glued - cyan, 600 needed.
Bracket - composed of one tripoint and three gems that are folded inwards and glued - gold and cyan, 2400 needed.
Flange - composed of two dits, one right handed and one left handed. It folds inwards - cyan, 7200 needed.
Tabs can be placed on the exposed sides of the pyramids, one tab can connect to walls to close each of the three gaps outside the pyramids and tabs can connect to the triangle faces of the slabs which will fold under the ike. All of these tabs are concave tabs. Convex tabs can be attached to the tiny triangle faces of the walls and caps that form a small star shaped area on the stellike, these will later connect to gears. Convex tabs are also connected to the isosceles pentagon faces of the walls. The stellike will fold inward at all folds except for the convex folds between the slabs and caps. The ike and slabs form a shallow ike bottomed dish. The pyramids, caps, and walls form trigon pyramid shaped cups - all together they form a stellated ike shaped rosette. Make 120 of these.
Next make the bulbs. Put concave tabs between the slates to close the gaps, also put concave tiles on the four faces inside the cavity that forms (two attach to tiles and two to slates). Convex tabs can connect to the tiny triangles on the tiles, and the outer triangles of the slates. Convex tabs also connect to the irregular pentagonal faces of the slates. The bulbs connect to the stellike between two trigon pyramid regions with convex folds, there will be 30 bulbs per stellike. Now cut out the 120 cages of death - this may take a good while.
We can describe the areas on the cage of death as follows: Footballs (the large lumps on the inside), spikes (tiny spike like things in the pentagonal holes), trigonic walls (walls facing the 3-fold region), pentagonic walls (walls facing the 5-fold regions), crowns (inverted pentagon faces in the 2-fold regions), the underside (the tetragonal faces on the inside, where there are ten coplanar faces for each pentagonal region). Place tabs on all faces of the spike (inward tabs facing inside and one outward tab outside), place convex tabs on the trigonic walls and the crowns. Also place concave tabs to the underside.
Now lets connect the stellike/bulb configuration into the center of the cage of death. The 30 bulbs will swallow the 30 footballs and have inward connections there. Every stellike needs one cage of death surrounding it as a base which will be corealmic to the ike and pyramid pieces.
We will need to create 720 carasels. Put concave tabs in the gaps (one tab for each gap) between two counters and convex tabs on the long outer face of the counters (which will connect to the pentagonic walls of a cage of death). Put convex tabs on the squares and kite faces of the gliders. Put convex tabs on the tiny trigonic faces on the counters as well as on the exposed faces of the bips. Put concave tabs on the inward tetragonal faces of the gliders. Cut out the carasels and fold them inwards except for the folds between a bip and a glider which fold convexly.
Now it is time to install the carasels into the cages of death - this is VERY tricky. Each carasel will lock in between two cages of death and each cage of death will have twelve carasels locked into them. The underneath section of the gears will connect to the cage of death's underside. The top of the gear will connect to the top of the cage's spikes, the bulbs at the irregular pentagon faces, the star shaped areas of the stellike, and the smallest faces of the bulbs. The strange hat-like face on the glider will attach to the trigonic walls of the cage of death. And finally, the long faces of the counters connect to the pentagonic walls. - now attach the second cage of death to the carasel in the same way. Connect the other 11 carasels to the first and then the second cage of death - keep going until all cages of death and carasels are attached - this thing is looking FREAKY! Notice that there are some small holes to fill in, so cut out the flanges (all 7200 of them) and glue them into the holes between the bottom side of the small spikes of the cages of death, the tops of the gears, the sides of the bulbs, and under the gliders at the tetragon faces. Each cage of death needs 60 flanges. Now all the cages of death are filled in.
Now lets log in the logs (OK, I know, my puns are bad, as bad as a member of the dot regiment). Put one concave tab to close the gap and convex tabs on the 12 trigonal and 6 tetragonal faces on each of the log's poles (no tabs needed on the equatorial area). Fold the logs inward and fit them between three carasels. The small equatorial triangles will connect to the small triangles of four counters where they meet on the carasels. The inverted pentagons connect to the crowns of the cage of death (three surrounding each log). Squares connect to gliders and the tabless triangles connect to the bips. Each carasel is now surrounded by 5 logs and each cage of death connects to 30 logs. Now make the 2400 brackets and the 600 spikups. The only tabs needed are to connect the gaps between the pieces of the combos (concave folds) and the golden (tripoint) trigonal pieces of the brackets (convex folds). The brackets will connect between three logs near the poles of them and they also connect to the gliders of three carasels. Their connections to logs and gliders are convex folds. The spikups fit in the 600 gaps between four logs at the log's poles and four brackets with convex folds.
The model is now complete - now let out a loud tribal yell (you'll need to after this model) and toss the crazy looking thing in the air and catch it in your arms as you swirl your arms in a polytwister sort of way.
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