| Two cube enneahedron | |
|---|---|
 Showing 6 red square faces, 3 yellow crossed-hexagon races (one in white). There is no central vertex. | |
| Faces | 9: 6 squares 3 self-crossing hexagons |
| Edges | 21 |
| Vertices | 14 |
| Euler characteristic | 2 |
| Convex hull | Stretched rhombic dodecahedron |
| Genus | 0 |
| Symmetry group | D3d, [2+,6], (2*3), order 12 |
| Rotation group | D3, [2,3]+, (233), order 6 |
| Dual polyhedron | Double-stacked octahedron |
| Properties | polycube |
In geometry, a two-cube enneahedron is a nonconvex enneahedron. It has 9 faces, 21 edges, and 24 vertices. With polyomino faces at right angles, it is a polycube. It has [2+,6] symmetry order 12, with three reflection plane, and 2-fold rotation axes.
Its Euler_characteristic is 2, a topological sphere. Its convex form can be seen as a triangular prism with the top and bottom triangles dissected with mid-edges and center into 3 coplanar kite faces. Its dual can be seen as two regular octahedra sharing a common face.
Construction
editAs a polycube it can be constructed as the union of 2 cubes with one comoon vertex. Coplanar neighboring squares are merged into polyominos, resulting in nine total faces: 6 square and 3 crossed-hexagons as 2 squared connected in a diagonal domino, 
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The enneahedron has 14 vertices, 4, 6, and 4 by planar levels. It has 24 edges.
Convex form
editThe geometry can be adjusted into a polyhedron with 3 regular hexagons in a loop, with 2 polar vertices added to make kite faces on top and bottom. It has D3h symmetry, order 12. It is similar to an elongated rhombic dodecahedron, which has 4-fold symmetry rather than 3-fold.
