This category contains the prisms of the uniform tilings. Well, except azip, whose prism is already in category A. The 52 other uniform tilings have their prisms here though. Their cells are two of the base tiling and prisms of the tiling faces, and their vertex figures are pyramids of their base's verf. Many of these are convex, these are the ones with convex tilings as their bases.
These are the prisms of the regular tilings. I'm also putting the fexat prism here, fexat is the compound of three hexats in the trat regiment. These act like truncates.
359. Squattip - Square tiling prism. Cells are cubes and 2 squats. Symbols include x4o4o x, o4x4o x, and x4o4x x. These are in the chon regiment.
360. Hexattip - Hexagonal tiling prism. Cells are hips and 2 hexats. Symbols include x6o3o x, x3x6o x, and x3x3x3*a x.
361. Trattip - Triangular tiling prism. Cells are trips and 2 trats. Symbol is x3o6o x.
C. Fexattip - Fissal hexagonal tiling prism. Cells are hips and 2 fexats. This is in the trattip regiment.
These are the prisms of the truncate tilings. These act like grombates.
362. Tosquattip - Truncated square tiling prism. Cells are cubes, ops, and 2 tosquats. Symbols are x4x4o x and x4x4x x. These can be found living in some higher symmetric regiments, usually with the ops blended into srohs.
363. Toxattip - Truncated hexagonal tiling prism. Cells are trips, twips, and 2 toxats. Symbol is x6x3o x.
364. Quitsquattip - Quasitruncated square tiling prism. Cells are cubes, stops, and 2 quitsquats. Symbols are x4/3x4o x and x4/3x4/3x x. These can be found living in some higher symmetric regiments, usually with the stops blended into srohs.
365. Quothattip - Quasitruncated hexagonal tiling prism. Cells are trips, stwips, and 2 quothats. Symbol is x6/5x3o x.
These are the prisms of the quasiregular tilings. These act like quasiregular truncates.
366. Shap - Square-hemiapeirogonal tiling prism. Cells are cubes, azips, and 2 shas. Symbol is x∞x4o4/3*a x. This is in the squattip regiment.
367. Ditathap - Ditrigonary triangular-hemiapeirogonal tiling prism. Cells are trips, azips, and 2 ditathas. Symbol is x3o3/2o∞*a x. This is in the trattip regiment.
368. Thattip - Trihexagonal tiling prism. Cells are trips, hips, and 2 thats. Symbol is o3x6o x. This and the next two form a regiment.
369. Thap - Triangular-hemiapeirogonal tiling prism. Cells are trips, azips, and 2 thas. Symbol is x∞x3o3/2*a x.
370. Hohap - Hexagonal-hemiapeirogonal tiling prism. Cells are hips, azips, and 2 hohas.
These are the prisms of the trapezivert tilings. These act like prismatorhombates. They form regiments of three.
371. Srothattip - Small rhombitrihexagonal tiling prism. Cells are trips, cubes, hips, and 2 srothats. Symbol is x3o6x x.
372. Shothattip - Small hexatrihexagonal tiling prism. Cells are trips, hips, twips, and 2 shothats. Symbol is x6x6/5o3*a x.
373. Srahttip - Small rhombihexagonal tiling prism. Cells are cubes, twips, and 2 srahts.
374. Ghothattip - Great hexatrihexagonal tiling prism. Cells are trips, hips, stwips, and 2 ghothats. Symbol is x6/5x6o 3*a x.
375. Qrothattip - Quasirhombitrihexagonal tiling prism. Cells are trips, cubes, hips, and 2 qrothats. Symbol is x3o6/5x x.
376. Grahttip - Great rhombihexagonal tiling prism. Cells are cubes, stwips, and 2 grahts.
377. Sossap - Small squarisquariapeirogonal tiling prism. Cells are cubes, stops, azips, and 2 sossas. Symbol is x4/3x4o∞*a x. These three can be found hiding in some higher symmetric regiments, often with the ops, stops, or both blended into srohs and grohs respectively.
378. Gossap - Great squarisquariapeirogonal tiling prism. Cells are cubes, ops, azips, and 2 gossas. Symbol is x4x4/3o∞*a x.
379. Sostip - Squarisquare tiling prism. Cells are ops, stops, and 2 sosts.
380. Shahap - Small hexahexaapeirogonal tiling prism. Cells are hips, stwips, azips, and 2 shahas. Symbol is x6/5x6o∞*a x.
381. Ghahap - Great hexahexaapeirogonal tiling prism. Cells are hips, twips, azips, and 2 ghahas. Symbol is x6x6/5o∞*a x.
382. Huhtip - Hexahexagonal tiling prism. Cells are twips, stwips, and 2 huhts.
These are the prisms of the omnitruncate tilings. These act like omnitruncates.
383. Grothattip - Great rhombitrihexagonal tiling prism. Cells are cubes, hips, twips, and 2 grothats. Symbol is x3x6x x.
384. Qrasquittip - Quasirhombated square tiling prism. Cells are cubes, ops, stops, and 2 qrasquits. Symbol is x4x4/3x x. These can be found hiding in some higher symmetric regiments, often with the ops, stops, or both blended into srohs or grohs respectively.
385. Quitothittip - Quasitruncated trihexagonal tiling prism. Cells are cubes, hips, stwips, and 2 quitothits. Symbol is x3x6/5x x.
386. Thotithittip - Trihexatruncatred trihexagonal tiling prism. Cells are hips, twips, stwips, and 2 thotithits. Symbol is x6x6/5x3*a x.
387. Satsap - Squariapeirotruncated squariapeirogonal tiling prism. Cells are ops, stops, azips, and 2 satsas. Symbol is x4x4/3x∞*a x. These can be found hiding in some higher symmetric regiments, often with the ops, stops, or both blended into srohs or grohs respectively.
388. Hathap - Hexaapeirotruncates hexaapeirogonal tiling prism. Cells are twips, stwips, azips, and 2 hathas. Symbol is x6x6/5x∞*a x.
These are the prisms of the snub tilings.
389. Snasquattip - Snub square tiling prism. Cells are cubes, trips, and 2 snasquats.
390. Snathattip - Snub trihexagonal tiling prism. Cells are trips in two orbits, hips, and 2 snathats.
391. Rasisquattip - Retrosnub square tiling prism. Cells are cubes, trips, and 2 rasisquats.
392. Snassap - Snub squarisquariapeirogonal tiling prism. Cells are trips, cubes in two orbits, azips, and 2 snassas.
These are the prisms of the laminate tilings, except azip, whose prism is in Category A.
393. Azappip - Apeirogonal antiprism prism. Cells are trips, 2 azips, and 2 azaps. Can also be called the apeirogonal antiduoprism. This may be the only uniform honeycomb with two orbits of cells in finite amounts.
394. Etrattip - Elongated triangular tiling prism. Cells are trips, cubes, and 2 etrats. There are blends of these we will see later, and the same for its conjugate below.
395. Retrattip - Retroelongated triangular tiling prism. Cells are trips, cubes, and 2 retrats.
These are the prisms of the blended tilings. Their verfs are about as wacky as can be, for pyramids. They align into regiments the same way their bases do: sets of 2, 6, 6, and 1.
396. Sarattip - Snub rhombiapeirogonal tiling prism. Cells are trips, cubes, azips, and 2 sarats.
397. Rasrattip - Retrosnub rhombiapeirogonal tiling prism. Cells are trips, cubes, azips, and 2 rasrats.
398. Rassersap - Rhombisnub squarirhombisquariapeirogonal tiling prism. Cells are cubes in two orbits, stops in two orbits, azips, and 2 rassersas.
399. Rarsisresap - Rhombiretrosnub squarirhombisquariapeirogonal tiling prism. Cells are cubes in two orbits, ops in two orbits, azips, and 2 rarsisresas.
400. Rosassap - Rhombisnub squarisquariapeirogonal tiling prism. Cells are cubes, ops, stops, azips, and 2 rosassas.
401. Rorisassap - Rhombiretrosnub squarisquariapeirogonal tiling prism. Cells are cubes, ops, stops, azips, and 2 rorisassas.
402. Rasishrap - Rhombisnub squarihyperrhombiapeirogonal tiling prism. Cells are cubes in two orbits, stops, azips, and 2 rasishras.
403. Rarsishrap - Rhombiretrosnub squarihyperrhombiapeirogonal tiling prism. Cells are cubes in two orbits, ops, azips, and 2 rarsishras.
404. Sishahap - Small snub hexahexaapeirogonal tiling prism. Cells are trips, hips, stwips, azips, and 2 sishahas.
405. Sarshahap - Small retrosnub hexahexaapeirogonal tiling prism. Cells are trips, hips, stwips, azips, and 2 sarshahas.
406. Gishahap - Great snub hexahexaapeirogonal tiling prism. Cells are trips, hips, twips, azips, and 2 gishahas.
407. Garshahap - Great retrosnub hexahexaapeirogonal tiling prism. Cells are trips, hips, twips, azips, and 2 garshahas.
408. Rodsattip - Rhombidisnub apeirogonal tiling prism. Cells are trips, cubes, azips, and 2 rodsats.
409. Roridsattip - Rhombiretrodisnub apeirogonal tiling prism. Cells are trips, cubes, azips, and 2 roridsats.
410. Irdsattip - Inverted rhombidisnub apeirogonal tiling. Cells are trips, cubes, azips, and 2 irdsats.
The prisms are self conjugate if their bases are. Please refer to the tiling pages for futher information.
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