Toroidal blend of 8 dodecahedra
|Toroidal blend of 8 dodecahedra|
|Faces||4+4+4+8 +4+4+4+8 +4+4+8+8+8+8 pentagons|
|Edges||2+2+4+4+8+8+8+8+8+8 +2+2+4+4+8+8+8+8+8+8 +4+4+8+8+8+8+8+8+8+8+8|
|Vertices||4+4+4+4+8+8+8 +4+4+4+4+8+8+8 +8+8+8+8+8|
|Vertex figures||4+4+4+4+4+4+4+8+8+8+8+8+8+8 triangles, edge length (1+√)/2|
|Measures (edge length 1)|
|Number of external pieces||80|
|Level of complexity||20|
|Convex hull||Minkowski sum of dodecahedron with edge length 1 and rhombus with edge length and diagonal ratio (1+√)/2, where the diagonals are parallel to edges of the dodecahedron|
|Abstract & topological properties|
|Symmetry||K3, order 8|
The toroidal blend of 8 dodecahedra is a Stewart toroid that consists of 80 pentagons. It can be obtained by outer-blending eight dodecahedra together in a rhombus-shaped loop. The four dodecahedra at the vertices of the virtual rhombus are all oriented in the same way.
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The shape of this toroid differs from the toroidal blend of 8 octahedra: the latter's virtual rhombus has a diagonal ratio of √, while this one's has diagonal ratio (1+√)/2.
Thirty copies of the toroid can be blended together, each blending pair coinciding at three dodecahedra with collinear centers, to form a toroidal blend of 92 dodecahedra with dodecahedral symmetry and an appearance like the skeleton of a rhombic triacontahedron.