D4.6 (EntityTopic, 15)
From Hi.gher. Space
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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 (J91's) 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 cuboctahedra become triangular cupolae. | 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 (J91's) 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 cuboctahedra become triangular cupolae. | ||
- | ==Projections== | + | == Projections == |
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Side-view showing equatorial cells: | Side-view showing equatorial cells: | ||
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<[#embed [hash 4C4DG39H89GXR5QJMJSXA2DHF5]]> | <[#embed [hash 4C4DG39H89GXR5QJMJSXA2DHF5]]> | ||
- | ==Stella4D model== | + | == Stella4D model == |
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[http://hddb.teamikaria.com/dl/K5JJP2HQ9F54T8K231H9YJNWS3.off .off file] | [http://hddb.teamikaria.com/dl/K5JJP2HQ9F54T8K231H9YJNWS3.off .off file] |
Revision as of 02:29, 23 February 2014
CJ4.6 is a CRF polychoron crown jewel discovered by student91 on February 18, 2014. It is a modification of the hydrocantichoron o5x3o3x, where 30 icosidodecahedra 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 (J91's) 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 cuboctahedra become triangular cupolae.
Projections
Side-view showing equatorial cells:
Top-view with highlighted equatorial cells: