D4.6 (EntityTopic, 15)
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| - | + | D4.6 is a [[bilbirothawroid]] discovered by [[student91]] on February 18, 2014. It is a modification of the [[hydrocantichoron]] o5x3o3x, where 30 [[rhodomesohedra]] are replaced by [[bilunabirotunda]]e (J91), with the resulting non-CRF parts substituted by CRF patches containing 12 rosettes of 5 [[hexagonal prism]]s alternating with 5 [[truncated tetrahedra]] encircling pillars of [[pentagonal prism]]s capped by [[pentagonal rotunda]]e. | |
Its construction is as follows: delete the vertices from o5x3o3x of edge length 2, whose first coordinate is less than the Golden Ratio φ or is equal to 2, then push the remaining vertices together (i.e., if the first coordinate is ≥φ then subtract φ; if it's ≤-φ then add φ). The vertices whose original first coordinates were φ become coincident. Then new points x5o3A are added with first coordinates ±1, where A=6φ. These modifications of o5x3o3x cause a reduction of its equatorial cells into 30 bilunabirotunda (J91s) in icosahedral symmetry, with the 12 gaps between them filled by circles of alternating hexagonal prisms and truncated tetrahedra surrounding a pentagonal prism with pentagonal cupolae above and below it. Twelve of the o5x3o's near the equatorial layer are truncated into pentagonal rotundae, and a number of [[stauromesohedra]] become [[triangular cupola]]e. | Its construction is as follows: delete the vertices from o5x3o3x of edge length 2, whose first coordinate is less than the Golden Ratio φ or is equal to 2, then push the remaining vertices together (i.e., if the first coordinate is ≥φ then subtract φ; if it's ≤-φ then add φ). The vertices whose original first coordinates were φ become coincident. Then new points x5o3A are added with first coordinates ±1, where A=6φ. These modifications of o5x3o3x cause a reduction of its equatorial cells into 30 bilunabirotunda (J91s) in icosahedral symmetry, with the 12 gaps between them filled by circles of alternating hexagonal prisms and truncated tetrahedra surrounding a pentagonal prism with pentagonal cupolae above and below it. Twelve of the o5x3o's near the equatorial layer are truncated into pentagonal rotundae, and a number of [[stauromesohedra]] become [[triangular cupola]]e. | ||
Revision as of 15:30, 1 March 2014
D4.6 is a bilbirothawroid discovered by student91 on February 18, 2014. It is a modification of the hydrocantichoron o5x3o3x, where 30 rhodomesohedra are replaced by bilunabirotundae (J91), with the resulting non-CRF parts substituted by CRF patches containing 12 rosettes of 5 hexagonal prisms alternating with 5 truncated tetrahedra encircling pillars of pentagonal prisms capped by pentagonal rotundae.
Its construction is as follows: delete the vertices from o5x3o3x of edge length 2, whose first coordinate is less than the Golden Ratio φ or is equal to 2, then push the remaining vertices together (i.e., if the first coordinate is ≥φ then subtract φ; if it's ≤-φ then add φ). The vertices whose original first coordinates were φ become coincident. Then new points x5o3A are added with first coordinates ±1, where A=6φ. These modifications of o5x3o3x cause a reduction of its equatorial cells into 30 bilunabirotunda (J91s) in icosahedral symmetry, with the 12 gaps between them filled by circles of alternating hexagonal prisms and truncated tetrahedra surrounding a pentagonal prism with pentagonal cupolae above and below it. Twelve of the o5x3o's near the equatorial layer are truncated into pentagonal rotundae, and a number of stauromesohedra become triangular cupolae.
Projections
Side-view showing equatorial cells:
Top-view with highlighted equatorial cells:
