Bezdek's Unistable Polyhedron With 18 Faces

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top z
86.9
bottom z
-49.5
choose face
17
show normal
opacity
plot range
50
Does the normal on the face 17 intersects it? True
The number of stable faces: 1
This Demonstration shows Bezdek's unistable polyhedron with 18 faces. A face is stable if, and only if, the orthogonal projection (red point) of the center of mass (black point) onto the face lies inside the face. A unistable polyhedron has only one stable face. The polyhedron is a skew pyramid placed along the
z
axis and can be changed using the
z
sliders.

Details

Guy constructed unistable 19-faces solid in 1968[2, 3, 4]. Bezdek found unistable 18-faces solid in 2011[1]. In[5] Reshetov constructed unistable polyhedra with 14, 15, 16, and 17 faces.

References

[1] A. Bezdek, On stability of polyhedra, Workshop on Discrete Geometry, 13-16 September 2011, Fields Institute, Canada (2011), pp. 2490-2491.
[2] J. Bryant and C. Sangwin, How Round Is Your Circle?: Where Engineering and Mathematics Meet, Princeton: Princeton University Press, 2008 pp. 273–276.
[3] R. K. Guy, A Unistable Polyhedron, Calgary: University of Calgary Department of Mathematics, 1968.
[4] J. H. Conway, M. Goldberg, and R. K. Guy, Problem 66-12, SIAM Review 11, 1969 pp. 78–82.
[5] A. Reshetov, A Unistable Polyhedron with 14 Faces, International Journal of Computational Geometry & Applications, Vol. 24, No. 1 (2014) pp. 39-59.

External Links

Unistable Polyhedron (Wolfram MathWorld)
Some Unistable Polyhedra
Reshetov's Unistable Polyhedra with 14, 15, 16, and 17 Faces

Permanent Citation

Izidor Hafner
​
​"Bezdek's Unistable Polyhedron With 18 Faces"​
​http://demonstrations.wolfram.com/BezdeksUnistablePolyhedronWith18Faces/​
​Wolfram Demonstrations Project​
​Published: December 9, 2015