|Bowers style acronym||Hihipap|
|Coxeter diagram||x6s2s12o ()|
|Cells||36 wedges, 12 ditrigonal trapezoprisms, 6 hexagonal prisms, 6 hexagonal antiprisms|
|Faces||72 isosceles triangles, 72 isosceles trapezoids, 36 rectangles, 12 hexagons, 12 ditrigons|
|Vertex figure||Monoaugmented isosceles trapezoidal pyramid|
|Measures (as derived from unit-edge dodecagonal duoprism)|
|Edge lengths||Short edges of ditrigons (36): 1|
|Side edges (72):|
|Edges of hexagons (72):|
|Long edges of ditrigons (36):|
|Abstract & topological properties|
|Symmetry||(G2×I2(12))/2, order 144|
The hexagonal-hexagonal prismantiprismoid or hihipap, also known as the edge-snub hexagonal-hexagonal duoprism or 6-6 prismantiprismoid, is a convex isogonal polychoron that consists of 6 hexagonal antiprisms, 6 hexagonal prisms, 12 ditrigonal trapezoprisms, and 36 wedges. 1 hexagonal antiprism, 1 hexagonal prism, 2 ditrigonal trapezoprisms, and 3 wedges join at each vertex. It can be obtained through the process of alternating one class of edges of the dodecagonal duoprism so that one ring of dodecagons become ditrigons. However, it cannot be made uniform, as it generally has 4 edge lengths, which can be minimized to no fewer than 2 different sizes.
Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.74436.
Vertex coordinates[edit | edit source]
The vertices of a hexagonal-hexagonal prismantiprismoid based on a dodecagonal duoprism of edge length 1, centered at the origin, are given by: