Chapter 9 - (R)(A)(Q)(T) Models Based on Prisms

  • This chapter includes models that are (T) and based on prisms (and prism variations) removed from other polyhedra. It also includes models that are not (T), that are rings (or other conglomerations) of prisms, that result in a (R)(A)(Q) model.
    Model.Stel GenusProperties Pages with Diagram Pages with DescriptionNotes
    (30P5Y5-30E)+(24P3Y3-24E) .Stel7 (R)(A)(D)84 rings
    R5P10R5 / Q5P10 .Stel1 (R)(A)(Q)(T)(D)86 4-5-10-5 - J42 / J20
    R5P10R5 / Q5P10v2 .Stel1 (R)(A)(Q)(T)(D)86 3-5-10-5 - J42 / gJ20
    R5P10gR5 / Q5P10 .Stel1 (R)(A)(Q)(T)(D)86 J43 / J20
    R5P10R5 / Q5P10Q5 .Stel1 (R)(A)(Q)(T)(D)86 4-5-4-5 - J42 / J38
    R5P10R5 / Q5P10Q5v2 .Stel1 (R)(A)(Q)(T)(D)86 3-5-3-5 - J42 / gJ38
    R5P10gR5 / Q5P10Q5 .Stel1 (R)(A)(Q)(T)(D)86 J43 / J38
    R5P10R5 / Q5P10gQ5 .Stel1 (R)(A)(Q)(T)(D)86 J42 / J39
    R5P10gR5 / Q5P10gQ5 .Stel1 (R)(A)(Q)(T)(D)86 J43 / J39
    R5P10R5 / Q5P10 / P5Q5 .Stel2 (R)(A)(Q)(T)(D)87 4-5-4-5 - 2-Story - J42 / J20 / P5Q5
    R5P10R5 / Q5P10v2 / P5Q5 .Stel2 (R)(A)(Q)(T)(D)87 3-5-3-5 - 2-Story - J42 / gJ20 / P5Q5
    R5P10gR5 / Q5P10 / P5Q5 .Stel2 (R)(A)(Q)(T)(D)87 2-Story - J43 / J20 / P5Q5
    (J38...J43)=ln_ln .Stel1 ea (R)(A)(Q)(T)(D) 8814 different arrangements
    (J38...J43)=ln_ln_ln .Stel2 ea (R)(A)(Q)(T)(D)88 34 different arrangements
    more work to be done on p. 88 and 89       Not Exercises
    P6≈6P3 .StelNA NA 90dissection
    P12≈6P4⊕6P3⊕P6 .StelNA NA 90dissection
    (P12Y3-6EY4-6E) / P6 .Stel1 (R)(A)(Q)(D)90 H(P)=P12
    (P12Y3-6EP3-6E) / P6 .Stel1 (R)(A)(Q)(D)90 H(P)=P12
    (P30Y5-15EY3-15E) / S' .Stel1 (R)(A)(Q)(D)85, 90 H(P)=P30
    S' .Stel0 (A)(D)90 not regular-faced, short prism
    (P30Y5-15EY3-15E)-S'+bridge .Stel2 (R)(A)(Q)(D)91 H(P)=P30
    (P30Y5-15EY3-15E)-S'+2bridges .Stel4 (R)(A)(Q)(D)91 H(P)=P30
    4(P4Y4-E)+6(P3Y3-E) .Stel1 (R)(A)(Q)(D)92 not Q'' - irregular decagonal prism
    10(P5Y5-E)+12(P3Y3-E) .Stel1 (R)(A)(Q)(D)92 not Q'' - irregular 22-gonal prism
    6(P5Y5-E)+6(P3Y3-E) .Stel1 (R)(A)(Q)(D)92 not Q'' - irregular 15-gonal prism
    (P30Y515-EY315-E)-S'+3bridges .Stel5 (R)(A)(Q)(D)92 H(P)=P30

    Prev - Chapter 8 - Limiting Properties
    Next - Chapter 10 - The "K4-World"
    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).


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