Welcome to the web page for Polyhedra and Geometric Sculpture! Feel free to browse the photos of class work, or follow along with the course's progress. Please drop me an email with any questions or comments. Enjoy!

Feel free to download a draft of Polyhedra and Geodesic Structures for educational purposes. You may distribute it, but you may not sell it in any form.

Several updates have been made. All the graphics are completely redone!

If you use this text either for your own research or in the classroom, please email me and let me know. This information would be useful in garnering support from my school.

• [1] Tuesday, 17 Jan: Taking a tour of virtual polyhedra. Below are several sites with models of polyhedra and related structures.


• The models of Magnus Wenninger. Magnus Wenninger is the author of three influential books on polyhedra and spherical models.


• The sculpture of George Hart. Be sure to look at his Sculpture and Rapid Prototyping pages.


• The sculpture of Vladimir Bulatov. Be sure to look at his virtual polyhedra!


• Sculpture by Bathsheba. Read how they are made!


• What's a Q-Ball? Should we build an I-Ball?


• Tom Hull's origami. Watch his YouTube videos!


• Michal Kosmulski's modular origami.


• Russell Towle's POV-Ray-traced polyhedra.


• Mark Newbold's Waterman polyhedra.


• Flatland, the movie! We'll watch this later on this semester.



• [2] Wednesday, 18 Jan: Today, we're building the Platonic solids, deltahedra, and other convex polyhedra.
  
  Vocabulary you should be familiar with: convex polyhedron, Platonic solids (and their names), vertex (plural vertices), valence, edge, face, deltahedron, bipyramid, antiprism, compound, snub disphenoid, icosidodecahedron, Euler's formula, Schläfli symbol, duality. We'll discuss the remainder of these terms Friday!
  
  Read Chapter 2 for Friday. Bring scissors and glue tomorrow! (If you have them; I have some extra. But get them!) Also, read Chapter 2 on the Platonic solids.


• [3] Thursday, 19 Jan: Finish the icosahedron and dodecahedron by Monday. Please initial them as we will be storing them in the cabinet, and will be needing them for other work throughout the semester. Remember: these are our first models, so they will be graded on completion, more-or-less. And please, taping doesn't count. Yes, it's been tried before....


• [4] Friday, 20 Jan: Be prepared to present the solution to today's puzzle! And your models (intact and initialed) are due at the beginning of class Monday.

• [5] Monday, 23 Jan: You will need to have Mathematica working tomorrow. (Not having it will affect your participation grade.)


• [6] Tuesday, 24 Jan: Download today's introduction to graphics Mathematica notebook. (Note: You must first download the file to your Desktop (or other folder), and then open it.)
  
  Your assignment (cube + dodecahedron) is due Friday. Email to my IMSA email address your file of the form lastname_hw1.nb. Be creative! I will be looking for using some interesting graphics directives.


• [7] Thursday, 26 Jan: Download the Mathematica notebook on dual polyhedra. Don't forget the assignment due tomorrow (emailed to me by 4:15).


• [8] Friday, 27 Jan: Finish your models for Monday: one small model (12 faces), and one larger model (24 or 30 faces).

• [9] Monday, 30 Jan: Read Sections 9.1, 9.2, and 9.4 for Tuesday. Be prepared for an oral quiz.


• [10] Tuesday, 31 Jan:


• [11] Thursday, 2 Feb:


• [12] Friday, 3 Feb:

• [13] Monday, 6 Feb:


• [14] Tuesday, 7 Feb:


• [15] Thursday, 9 Feb:


• [16] Friday, 10 Feb: Be sure the first draft of your stellation is handed in by the end of class today!

• [17] Monday, 13 Feb: Finish the two-dimensional coordinates for the rhombic dodecahedron stellation diagram for Tuesday. Bring your laptops tomorrow!


• [18] Tuesday, 14 Feb:


• [19] Thursday, 16 Feb:

• [20] Tuesday, 21 Feb:


• [21] Thursday, 23 Feb: Buiding day tomorrow! Make sure you have your stellation model(s) finished by next Thursday.


• [22] Friday, 24 Feb: By next Thursday: finish the stellation project and the spherical dodecahedron.

• [23] Monday, 27 Feb: Bring your laptops for a Mathematica laboratory tomorrow! Also, here is the Mathematica notebook on geometric transformations. (Remember: You must save this file first on your computer, and then open it.)


• [24] Tuesday, 28 Feb:


• [25] Thursday, 1 Mar: Reminded: Class is cancelled tomorrow. Keep working on your Mathematica assignment!!


• [26] Friday, 2 Mar: For your Mathematica program due next Tuesday, you must email it to me at my IMSA email address. You should name your file lastname_mascot.nb, in a similar format to the last such homework assignment.

• [27] Monday, 5 Mar: Mascot due tomorrow! Look at Friday's post for the format.
  
  Be prepared for in-class work on your video tomorrow.


• [28] Tuesday, 6 Mar: You have until midnight tonight to submit your assignment!


• [29] Thursday, 8 Mar: Remember: the video project is due two weeks from Friday, which is March 23. This is Clash week, so plan ahead! (Which is why you have so long to do it.)
  
  Also, here is the list of video production tips from Bill McGrail.
  
  Read Flatland for Monday. No other homework until then!


• [30] Friday, 9 Mar: Don't forget: Flatland is due Monday!

• [31] Monday, 12 Mar: Remember: your Flatland essay is due next Monday. A good, full page on some interesting aspect of the book not fully explained. Be creative!


• [32] Tuesday, 13 Mar: Due date reminders: slide-togethers (Friday), short essay (Monday), and video (next Friday).


• [33] Thursday, 15 Mar: Slide-togethers due tomorrow!


• [34] Friday, 16 Mar: Remember: Essays due Monday. A FULL PAGE, and printed out BEFORE CLASS. Keep working on your video!

• [35] Monday, 19 Mar:


• [36] Tuesday, 20 Mar: We will be having the visitors from New York City Thursday. Be prepared to answer questions about your projects!


• [37] Thursday, 22 Mar: Videos tomorrow! Be prepared to bring your computer up and connect it to the projector.


• [38] Friday, 23 Mar: Be prepared to show your video Monday, if there is no power outage....

• [39] Monday, 26 Mar: Three students have still not handed in hard copies of Flatland essays. You know who you are!


• [40] Tuesday, 27 Mar:


• [41] Thursday, 29 Mar:


• [42] Friday, 30 Mar:

• [43] Tuesday, 10 Apr:


• [44] Thursday, 12 Apr:


• [45] Friday, 13 Apr:

• [46] Monday, 16 Apr:


• [47] Tuesday, 17 Apr: Just do the four problems (p. 256, 3(a)-(d)) for Monday, being sure you have both the three-dimensional drawing and the graph isomorphism drawn.


• [48] Thursday, 19 Apr: Icosahedral slide-togethers are due today.


• [49] Friday, 20 Apr:

• [50] Monday, 23 Apr:


• [51] Tuesday, 24 Apr: Don't forget to complete your (late!) graph theory assignments! Bring them Thursday.


• [52] Thursday, 26 Apr:


• [53] Friday, 27 Apr:

• [54] Monday, 30 Apr:


• [55] Tuesday, 1 May:


• [56] Wednesday, 2 May:


• [57] Thursday, 3 May:

• [58] Monday, 7 May:


• [59] Tuesday, 8 May:


• [60] Wednesday, 9 May:


• [61] Thursday, 10 May: