This is the simplest infinite category of uniform honeycombs, and it contains the prism products of the regular polygons and an apeirogon. Visually, these look like an infinitely tall stack of the n-gonal prism, with azips connecting to the infinite columns of squares. These are convex if the base polygon is. The apeirogon * apeirogon duoprism is super degenerate and blends into nothingness, so please do not call me asking where he went. I am only listing the ones here with at all relevant symmetries: ones based on 3, 4, 5, 6, 8, 10, and 12-gons. The other polygons definitely can be used as bases of these, but I don't care. Their verfs are all disphenoids, making them the closest thing batch has to friends.
These ones are convex. This means they are the duoprism of a convex polygon and an apeirogon.
Trazedip - Triangle-apeirogon duoprism. Cells are trips and 3 azips. Symbols are x3o x∞o and x3o x∞x.
Squazedip - Square-apeirogon duoprism. Cells are cubes and 4 azips. Symbols are x4o x∞o, x x x∞o, x4o x∞x, and x x x∞x. This is also the azip prism. Friends with chon!
Pazedip - Pentagon-apeirogon duoprism. Cells are pips and 5 azips. Symbols are x5o x∞o and x5o x∞x.
Hazedip - Hexagon-apeirogon duoprism. Cells are hips and 6 azips. Symbols are x6o x∞o, x3x x∞o, x6o x∞x, and x3x x∞x.
Oazedip - Octagon-apeirogon duoprism. Cells are ops and 8 azips. Symbols are x8o x∞o, x4x x∞o, x8o x∞x, and x4x x∞x. He can be found hiding within some more symmetric regiments, usually with the ops blended into srohs.
Deazedip - Decagon-apeirogon duoprism. Cells are dips and 10 azips. Symbols are x10o x∞o, x5x x∞o, x10o x∞x, x5x x∞x.
Doazedip - Dodecagon-apeirogon duoprism. Cells are twips and 12 azips. Symbols are x12o x∞o, x6x x∞o, x12o x∞x, and x6x x∞x.
N-azedip - N-gon-apeirogon duoprism. Cells are N-prisms and N azips. Symbols are xNo x∞o and xNo x∞x, and if N is even then also xN/2x x∞o and xN/2x x∞x.
These ones are nonconvex. This means they are the duoprism of a nonconvex polygon and an apeirogon.
Stazedip - Pentagram-apeirogon duoprism. Cells are stips and 5 azips. Symbols are x5/2o x∞o and x5/2o x∞x.
Stoazedip - Octagram-apeirogon duoprism. Cells are stops and 8 azips. Symbols are x8/3o x∞o, x4/3x x∞o, x8/3o x∞x, and x4/3x x∞x. He can also be found hiding in some more symmetric regiments, usually with the stops blended into grohs.
Stadeazedip - Decagram-apeirogon duoprism. Cells are stiddips and 10 azips. Symbols are x10/3o x∞o, x5/3x x∞o, x10/3o x∞x, and x10/3x x∞x.
Stadoazedip - Dodecagram-apeirogon duoprism. Cells are stwips and 12 azips. Symbols are x12/5o x∞o, x6/5x x∞o, x12/5o x∞x, x6/5x x∞x.
N/M-azedip - N/M-gon-apeirogon duoprism. Cells are N/M-prisms and N azips. Symbols are xN/Mo x∞o and xN/Mo x∞x, and if N is even then also x(N/2)/Mx x∞o and x(N/2)/Mx x∞x.
The following honeycombs are self conjugate: trazedip, squazedip, hazedip (all trivially).
The following form conjugate pairs: pazedip-stazedip, oazedip-stoazedip, deazedip-stadeazedip, doazedip-stadoazedip. In general, two polygon-apeirogon duoprisms are conjugate if their base polygons are.
Back to Honeycombs Home --- Category B
Site by Benjamin Klein, based on the work of Eric Binnendyk
contact me via emailbenklein at gmail dot com or on the Polytope Discord
Images by creeperman7002 using POV-Ray. Even disphenoids add to his radicality significantly.