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About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things, a large portion of which are geometrical. Welcome to my own little slice of the Internet. The viewpoints and opinions expressed on this website are my own. They should not be confused with those of my employer, nor any other organization, nor institution, of any kind.

Tessellation Using Regular Hexadecagons, Isosceles Trapezoids, Squares of Two Types, and Convex Pentagons

tess may 19 2015Another version, with the colors inverted:

tess may 19 2015

Sixteen Polyhedra with Cuboctahedral Symmetry

weird not goodUnnamed Dual UnnameIYd Dual Unnamed Dual x spring model het oy has tetraicosagons Dual of Convex adshgsdjl Dual of Convehgd x hull Dual hgdyg Convehgd x hull Dual hgdyg Cogddfnvehgd x hull creepy dual badly-truncated great rhombcuboctahedron -- fix it's dual badly-truncated great rhombcuboctahedron -- fix it! Augmented rhombcubocta 8 dodecagons and six octgons etc

I made these using Stella 4d, a computer program available at this website.

Revise, and Re-install, Unconscious Mental Subroutine

tess chiral 2012

Sleep eventually takes your awareness from you, and, at the end, you don’t even resist.

Asleep now. Initialization of nREM startup program in progress.

Stop. Evaluate time elapsed since last sleep-reprogramming. Identify areas of concern.

Rank items of concern in priority order,

Schedule upcoming REM cycle to allow the “playing out” out of necessary “real-word” drama to address the top priority concern. Maintain focus on that concern until it is replaced by another one, new, and of more importance. Keep an eye on all areas of past conflict, while watching for new ones, hoping for early detection.

If unavoidable, implement “the best you can fake it” multitasking coping-mode.

Realize that memory of this sleeping activity will be fragmentary at best.

Know also, nonetheless, that you are the one one writing the program, at both ends of the consciousness-spectrum, the autism spectrum, and any other spectra I find myself standing on.

To answer the obvious question: yes, this blog-post is deliberately being written in the grey zone between sleep and wakefulness. If parts of it make no sense, that’s the reason.

~~~

Note upon waking: I found this, written but not published, on my computer, when my alarm clock went off. I guess I’ll post it now!

A Chiral Tessellation, Using Regular Dodecagons, Regular Hexagons, Squares, and Rhombi (from 2012)

tess chiral 2012I have several “lost works” that I’m slowly finding and posting, from old jumpdrives, computers, little-known blogs, etc., and this is one of them. I made it in 2012, but few have seen it before now.

Two Compounds with Pyritohedral Symmetry: the Icosidodecahedron / Truncated Octahedron Compound, and the Rhombic Triacontahedron / Tetrakis Cube Compound

Compound of Icosidodeca and Trunc Octa its pyritohedralCompound of RTC and tetrakis cube its pyritohedral

Stella 4d, a program you can try here, was used to create these two compounds. Both have pyritohedral symmetry: the symmetry of a standard volleyball. The two compounds are also duals.

A Large Collection of Polyhedra with Icosidodecahedral Symmetry, Some of Them Chiral

A stellation of a faceted icosidodecahedron
Another nother2 stellation of a faceted icosidodecahedronAnother stellation of a faceted icosidodecahedronFaceted Stellated Triakibvjvsicosa
chiral 157th stellation of the icosidodecahedronAnother nother stellation of a faceted icosidodecahedronCompound of enantiomorphic pair of 157th stellations of IDnon-convex snub dodecahedron variantl12 irreg decagons 30 reg octagons 20 reg hexagons 60 isos trapezoids 122 totalll12 pentagon and 80 hexagons92 facesl302 faces including 12 pentadecagonsaug rid 1 of 2 Convex hullaug rid 2 of 2 Convex hullAugmented PHGolyAugmented PHGoly DUALCompound of enantiomorphic pairCompound of enantiomorphnb cnbic pairConsdhffgvex hullConvehxbvhvc hullConvejhfx hullConvenbvx hullConvex dfaljhullConvex hull of the base + dual model for the truncated dodecahedronConvex hullConvexbvhvc hullConvexsdjag hhgfullCoXCVNBnvex hulldual -- Faceted Compound of Compound of enantiomorphic pair and dualDual of Cohkhkjnvex hullDual of Cokhnvex hullDual of Cokjhihhkhkjnvex hullDual of Convex hullDual of Convexnvgxgc hullDual of CoXCVNBnvex hullDual ojhff Convex hullDual ojhjhff Convex hullFaceted Compound of enantiomorphic pairFaceted Convex hullFaceted DnvcualFaceted Dual
Faceted DualsgdhdFaceted DugffalFaceted DuhgdhggffalFaceted Great TriakisicosaFaceted RhombicosidodecgfshfsaFaceted Stellated Faceted DualFaceted Stellated Faceted DuhgdhgalFaceted Stellated Faceted Stellated Poly

I made these using Stella 4d, available here.

A Dodecahedron with Four Symetrically-Truncated Vertices

dodeca with 4 verts truncated tet symm

Dodecahedra have icosahedral (also called icosidodecahedral) symmetry. In the figure above, this symmetry is changed to tetrahedral, by truncation of four vertices with positions corresponding to the vertices (or, instead, faces) of a tetrahedron. The interchangeability of vertices and faces for the tetrahedron is related to the fact that the tetrahedron is self-dual.

[Image created using Stella 4d, available here.]

Symmetrically Shattering Glass

Symetrically shattering glass

Created with Stella 4d, available here.

Four Vases

four vases

Created with Stella 4d, a program available here.

Selections from the Stellation-Series of the Icosidodecahedron

The icosidodecahedron has a long and interesting stellation-series, and you can see the whole thing using Stella 4d, the program I used to make the rotating .gifs here. Rather than keep the scale the same in each frame, I set the program to make the polyhedron as large as possible, while still fitting in the image-box. This creates the illusion that the polyhedra below are “breathing.”

Glimpses of the invisible visible version 20th stellation of the icosidodecahedron

The polyhedron above is the 20th stellation of the icosidodecahedron — the one that appeared as the sole image in the last post here, but with completely different colors. The next one shown is the 31st stellation.

Glimpses of the invisible visible version 31st stellation of the icosidodecahedron

Glimpses of the invisible visible version 55th stellation of the icosidodecahedron

The 55th stellation is immediately above, while the next one is the 69th.

Glimpses of the invisible visible version 69th stellation of the icosidodecahedron

Glimpses of the invisible visible version 84th stellation of the icosidodecahedron

The 84th stellation is immediately above, while the next one is the 89th.

Glimpses of the invisible visible version 89th stellation of the icosidodecahedron

Glimpses of the invisible visible version 106th stellation of the icosidodecahedron

The 106th stellation is immediately above, while the next one is the the 110th.

Glimpses of the invisible visible version 110th stellation of the icosidodecahedron

Glimpses of the invisible visible version 135th stellation of the icosidodecahedron

The 135th stellation is immediately above, while the next one, which is chiral, is the 157th.

Glimpses of the invisible visible version 157th stellation of the icosidodecahedron