Chapter 10 - The "K₄-World"

In this chapter Stewart explores a whole world of figures based on K₄ - the Truncated Cuboctahedron - as the convex hull. This is a great figure for exploration, partly because it can be dissected completely, into Q₄'s, Q₃'s and P₄'s around a central E₄ - rhombicuboctahedron.

Model .Stel Genus Properties Pages with Diagram Pages with Description Notes 12P4(E4 / P4B4) .Stel 1 (R)(A)(D) 93   hole only K4≈E4⊕6Q4⊕8Q3⊕12P4 .Stel NA NA 95 94 dissection K4 - Height Face to Face .Stel NA NA 94   height comparisons K4 / 6Q4(E4) .Stel 5 (R)(A)(Q)(T)(D)   95, 97 cube face planes K4 / 8Q3(E4) .Stel 7 (R)(A)(Q)(T)(D)   95, 97 cube vertex planes K4 / 12P4(E4) .Stel 11 (R)(A)(Q)(T)(D)   95, 97 cube edge planes K4 / 4Q4(E4 / P4B4) .Stel 4 (R)(A)(Q)(T)(D)   96, 97 two storied K4 / 8Q3(E4 / P4B4) .Stel 8 (R)(A)(Q)(T)(D)   96, 97 two storied K4 / 12P4(E4 / P4B4) .Stel 12 (R)(A)(Q)(T)(D) 100, 136 96, 97, 100 two storied K4 / 12P4(E4 / P4B4) - construction .Stel NA NA 100   construction steps K4 / 4Q4(E4 / d(P4B4)) .Stel 4 (R)(A)(Q)(T)(D)   108, 109 two storied, d=delta K4 / 6Q3(E4 / d(P4B4)) .Stel 6 (R)(A)(Q)(T)(D)   108, 109 two storied, d=delta K4 / 10P4(E4 / d(P4B4)) .Stel 10 (R)(A)(Q)(T)(D)   108, 109 two storied, d=delta more work to be done on p. 110 through 118           Ex. 56-77 K4Q4-4E - AlongsideTunnels .Stel NA NA 119   showing unit height bands K4 / Q4(B4P4)Q4 .Stel 1 (R)(A)(Q)(T)(D) 119   no excavations K4 / gQ4g(B4P4)gQ4 .Stel 1 (R)(A)(Q)(T)(D) 119   no excavations K4Q44E / Q4(B4P4)Q4 .Stel 1 (R)(A)(Q)(D) 119   with Q4 excavations K4Q44E / gQ4g(B4P4)gQ4 .Stel 1 (R)(A)(Q)(D) 119   with Q4 excavations K4' / Q4(B4)Q4 .Stel 1 (R)(A)(Q)(D) 119   minus the unit height bands - not Q'' K4'-gQ4g(B4)gQ4 .Stel 1 (R)(A)(Q)(D) 119   minus the unit height bands - not Q'' more work to be done on p. 120 through 124           Ex. 79-91 Prev - Chapter 9 - (R)(A)(Q)(T) Models Based on Prisms Next - Chapter 11 - The Bilunabirotunda, J91 Back to Adventures Among the Toroids - Index Disclaimer: These pages are dedicated to B.M. Stewart. They are intended to be used by readers of his book to better illustrate his ideas in three dimensions. His book has tons of information that I do not intend to represent here, and I highly encourage anyone interested in this subject to buy the book. If you like my illustrations, please let me know. And if you are interested in a particular Stewart Toroid being modeled, please let me know and I will do what I can. Thanks also to Robert Webb for his very cool "Stella" program. I have used it extensively to generate VRML files for my site. It is a great tool for rapid exploration of augmentations and excavations of polyhedra (among other things). Back to the main Polyhedron Page. Link to this page as http://Polyhedra.Doskey.com/Stewart10.html Alexander's Polyhedra, (c) 1998-2006, Alex Doskey