Solving the Holyhedron

A holyhedron is a polyhedron with each face containing at least one polygon shaped hole. The boundaries of the holes share no point with each other or the boundary of the faces. For example, consider a solid cube with its 6 faces. Next, imagine thrusting a pentagonal rod through 1 face, all the way through the cube to the other side to produce (for example) a pentagonal tunnel, and only 2 of those 11 faces have holes punched in them. Each time we punch a hole, we are creating more faces. The immense challenge to finding a holyhedron is to make the holes such that they eventually punch through more than one face to reduce the number of faces that have no holes.

The holyhedron concept was first introduced by Princeton mathematician John h Conway in the 1990’s, who offered a prize of USD 10,000 to anyone who could find such an object. He also stipulated that this cash reward would be divided by the number of faces in such an object. In 1997, David W Wilson coined the word holyhedron to indicate a hole filled polyhedron.

Finally, in 1999, American mathematician Jade P. Vinson discovered the world’s first holyhedron specimen with a total of 78,585,627 faces. John Conway has offered a prize of $10000 divided by the number of faces, so this one should be worth approximately $20.3252.

(The Math book, Clifford A. Pickover, PhD Yale)

Domnita and me are a part of Cluj painting club. Last evening we were at the 5 year anniversary. We as capital market researchers don’t make the group as diverse as Dr. S. Istvan. 75 paintings were exhibited. The one above was painted by Istvan. When I saw it, I told him it was a holyhedron. It might look like coincidence but the mathematics we know is a lot about patterns and structures. If there is something mathematical, you will find it in nature. This is why John’s prize money was up for grabs, the moment it was announced. Why is nature mathematical? Because nature is proportional. Nature has all proportions, infinitesimally large and infinitesimally small. Time does not destroy the proportion of nature, even when nature ages, grows and decays. Then why no credit for Time in assisting nature to retain its proportion? Does it not sound intuitive that because Time is proportional, nature mirrors it and mathematics proves it. Time created nature and humans invented mathematics to study and solve the beautiful holyhedron.




  1. Bharat
    Bharat at |

    Talking about time reminds me of Mahabharat (Indian Mythology). I am not sure if Mukul has seen it and noticed, but it just struck me when I read this article. The chracter used to narrate the story of Mahabharat is actually time (Main samay hoon). How about a coincidence there?

  2. Orpheus
    Orpheus at |

    Yes. I missed it. I remember now.
    -Main Samay Hoon-

    Thanks Bharat


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