These 15 tilings are formed through blends of other tilings in complex and nonobvious manners. Their constructions vary throughout the category, making this essentially a misc category with the uncategorizable and odd tilings. There are 2 with laminate symmetry and close relations to etrat and retrat, 6 with various squattic subsymmetries in the sossa superregiment, 6 with hexattic symmetry in the shaha superregiment, and one odd thing with kicyclotriggic symmetry and mild relation to the laminates. I know that the non-ionic members of the sossa superregiment are used in nonprismatic honeycombs, and the hexattics probably aren't, but the laminates, ionic sossas, and kicyclotriggic guy may or may not have use.
These are formed by blending a compound of ditathas with rows of azips. Imagine taking a ditatha, copying it, and moving the copy sideways half an edge and then down until the apeirogons between the two ditathas align 1 unit apart into azips. Then you can blend the ditathas together with the azips as a bridge, and the whole thing has laminate symmetry. You might think you could do the same with shas being bridged by azaps, but it doesn't come out isogonal.
39: Sarat - Snub rhombiapeirogonal tiling. Its faces are triangles, squares, and apeirogons. This blends the azips onto the 2 ditathas in a ""more prograde"" manner that looks more like etrat.
40: Rasrat - Retrosnub rhombiapeirogonal tiling. Its faces are triangles, squares, apeirogons. This blends the azips onto the 2 ditathas in a ""more retrograde"" manner that looks more like retrat.
The sossa regiment has bonus edges you can draw in the vertices that are also unit length. Using these edges reveals a hidden compound of 4 square tilings in the regiment. Taking sossa under various subsymmetries allows these squats to turn into shas, which can then blend with the apeirogons in the sossas to make new uniform tilings.
41: Rassersa - Rhombisnub squarirhombisquariapeirogonal tiling. Its faces are squares in two orbits, octagrams in two orbits, and apeirogons. This is a blend of sossa with 4 shas, with the sossas taken under kaleidoscopic omnitruncate symmetry with an irregular quadrilateral verf. Despite being half symmetry, it is still squattic symmetry, because euclideans be like that. This symmetry can be easily visualized by imagining sossa as a faceting of tosquat, and then treating the tosquat as an omnitruncate as x4x4x. Noble fans would call this thing's vertex figure a "pravogram".
42: Rarsisresa - Rhombiretrosnub squarirhombisquariapeirogonal tiling. Its faces are squares in two orbits, octagons in two orbits, and apeirogons. This is a blend of gossa with 4 shas, with the sossas as kaleidoscopic omnitruncates again. Noble fans would call this thing's verf a "kipropellogram".
43: Rosassa - Rhombisnub squarisquariapeirogonal tiling. Its faces are squares, octagrams, octagons, and apeirogons. This is a blend of 2 satsas with 4 shas. This can be done because sossa as a kaleidoscopic omnitruncate contains a 2-satsa compound. It also contains qrasquit, but it can't blend here, since it has no apeirogons. This one blends the satsas into the shas in a ""more prograde"" manner with the snub squares attaching to octagrams progradely. Noble fans would call this thing's verf a "kipiscoid"
44: Rorisassa - Rhombiretrosnub squarisquariapeirogonal tiling. Its faces are squares, octagrams, octagons, and apeirogons. This is also a blend of 2 satsas with 4 shas. The reason there are two different blends here is that the shas have two orientations in the regiment, because of the half symmetry, and the satsas have two orientations in the regiment, because of the half symmetry, so you can swap the orientation of one but not the other to get a completely different tiling. This one blends the satsas into the shas in a ""more retrograde"" manner with the snub squares attaching to octagrams retrogradely. Noble fans would call this thing's verf a "kisombreroid"
45: Rasishra - Rhombisnub squarihyperrhombiapeirogonal tiling. Its faces are squares in two orbits, octagrams, and apeirogons. This is also a blend of sossa with 4 shas, and its vertex figure is identical to rassersa. The difference is that instead of taking sossa under the kaleidoscopic omnitruncate symmetry, you take it under an ionic symmetry, sort of like considering gocco under pyritic. This maintains isogonality, and continues to cause the squats' squares to split in half so they can become shas, but the shas are oriented differently than in rassersa, and the faces are on different symmetry axes. Notably, the octagrams are on mere rhombic axes. I call the ionic squattic symmetry "iosquattic", we saw it earlier in category 6.
46: Rarsishra - Rhombiretrosnub squarihyperrhombiapeirogonal tiling. Its faces are squares in two orbits, octagons, and apeirogons. This is also a blend of gossa with 4 shas, and the vertex figure is identical to rarsisresa. This is explained by the exact same logic as rasishra existing, just now the sossas are gossas. Still iosquattic. Unfortunately, you can't blend satsas with ionic symmetry, as the 2satsa compound only works under the kaleidoscopic omnitruncate symmetry, since it requires the octagons and octagrams to split into 2 types.
These are formed in a similar manner to the sossa superregiment. There are extra unit edges you can draw in the vertices of shaha, and using them reveals a hidden compound of 4 trats. This time, subsymmetry is not needed, the trats are already under a low enough symmetry to become ditathas. Then the ditathas can blend with the shaha members on apeirogons, in two orientations. There also happen to be hidden azips in this regiment, which makes another two members that are more laminate-y. Under ionic subsymmetry, you can find compounds of 6 sarats and rasrats here, but nothing actually cool. All the real things here are hexattic. I should also mention this regiment contains an exotic uniform compound of hexagonal cupolae (or retrocupolae), which is awesome I think. All of the vertex figures here are various strange octagons with bilateral symmetry that nobody dares to name.
47: Sishaha - Small snub hexahexaapeirogonal tiling. Its faces are triangles, hexagons, dodecagrams, and apeirogons. This is a blend of shaha and 4 ditathas in a ""more prograde"" manner, with the dodecagrams attaching to the triangles progradely.
48: Sarshaha - Small retrosnub hexahexaapeirogonal tiling. Its faces are triangles, hexagons, dodecagrams, and apeirogons. This is a blend of shaha and 4 ditathas in a ""more retrograde"" manner, with the dodecagrams attaching to the triangles retrogradely.
49: Gishaha - Great snub hexahexaapeirogonal tiling. Its faces are triangles, hexagons, dodecagons, and apeirogons. This is a blend of ghaha and 4 ditathas in a ""more prograde"" manner, with the dodecagons attaching to the triangles progradely.
50: Garshaha - Great retrosnub hexahexaapeirogonal tiling. Its faces are triangles, hexagons, dodecagons, and apeirogons. This is a blend of ghaha and 4 ditathas in a ""more retrograde"" manner, with the dodecagons attaching to the triangles retrogradely.
51: Rodsat - Rhombidisnub apeirogonal tiling. Its faces are triangles, squares, and apeirogons. This is a blend of 4 ditathas with endless azips in a ""more prograde"" manner, with squares connecting to triangles progradely. This is sorta related to sarat, being somewhat derivable as a compound of 12 sarats with the ditathas on each fused together.
52: Roridsat - Rhombiretrodisnub apeirogonal tiling. Its faces are triangles, squares, and apeirogons. This is a blend of 4 ditathas with endless azips in a ""more retrograde"" manner, with squares connecting to triangles retrogradely. This is somewhat related to rasrat in the same way the above tiling is related to sarat.
53: Irdsat - Inverted rhombidisnub apeirogonal tiling. Its faces are triangles, squares, and apeirogons. Its vertex figure is an awful-looking chiral octagon. Irdsat is.. weird. Its convex hull is an s6s3o, which is a symmetry i call "iohexattic", but irdsat itself is chiral and thus only has kicyclotriggic symmetry. It has some derivation as a componund of 3 sarats or rasrats with ditathas fused together. It is a blend of 3 ditathas and endless azips, but the azips are simultaneously prograde and retrograde to the triangles, while remaining in one orbit. Swapping the orientation of the ditatha results in the exact same tiling, due to the s6s3o supersymmetry. This tiling has a Random Bonus Triangle in its edges that it never uses in either orientation. Irdsat is extremely, extremely weird. I hope someday we use it in honeycombs.
Below shows how the blends pair up as conjugates. Some of these are honestly just guesses.
Conjuates:
The following are self-conjugate: irdsat
The following are conjugate pairs: srarat-rasrat, rassersa-rarsisresa, rosassa-rorisassa, rasishra-rarsishra, sishaha-garshaha, sarshaha-gishaha, rodsat-roridsat.
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