Download presentation
Presentation is loading. Please wait.
1
Wish upon a Stellated Dodecahedron
Ethan Bolker Family Friday National Museum of Mathematics July 12, 2019
2
quintessence air fire earth water Plato
3
Paolo Ucello? Venice Basilica of St. Mark ~1430
4
Johannes Kepler Harmonice Mundi 1619
5
Kepler’s Echinus
6
Echinus = hedgehog http://bestiary.ca/beasts/beastgallery217.htm#
Bestiarius - Bestiary of Anne Walsh Kongelige Bibliotek (National Library of Denmark)
7
Edible sea urchin Echinus esculentus 20cm
8
Mathematical Snapshots
Hugo Steinhaus Mathematical Snapshots Stechert 1937 Oxford 1950 Dover 1999
9
Build a stellated dodecahedron?
10
Cundy and Rollett, with construction tips
Net Cundy and Rollett, with construction tips
12
{Picture of the new pentagrams}
Use 12 of these {Picture of the new pentagrams}
13
Voila!
15
great stellated dodecahedron
Kepler’s Ostrea (Jamnitzer 1568) great stellated dodecahedron
16
Why oyster? Search google (books) for Ostrea Kepler, find
Joannis Kepleri astronomi opera omnia
17
Twist a pyramid
18
Twist a star
19
Rubik’s stellated dodecahedron
Scramble, try to unscramble Harder than Rubik’s cube? What configurations are possible? Swap stars and pyramids?
20
Gadget vs. cube 6 colors 60 facets 6 axes 24 degree 5 moves
Swap any pair of facets Pyramids (stars) commute, usually with each other too 6 colors 54 facets 3 axes 18 degree 4 moves Swap any pair of centers, edges, corners Only rotations about the same axis commute
21
Gadget vs. cube 6 colors 60 facets 6 axes 24 degree 5 moves
Swap any pair of facets Pyramids (stars) commute, usually with each other too 6 colors 54 facets 3 axes 18 degree 4 moves Swap any pair of centers, edges, corners Only rotations about the same axis commute
22
The gadget group Acts as a group of permutations of the 60 facets
Kernel has order 120 ×10!6 = 2.7 × 1041 Configuration space 60!/|kernel| ~ 3 × 1040 Study action: orbits, macros David Joyner: Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other Mathematical Toys
Similar presentations
© 2025 SlidePlayer.com Inc.
All rights reserved.