To enter a query, please send an e-mail to This email address is being protected from spambots. You need JavaScript enabled to view it.. You may include images as well.

Date: Wed, 12 Jul 2006
From: This email address is being protected from spambots. You need JavaScript enabled to view it.

I really want to know about polyhedra in/on churches.

(a) It is very common in Hungary that the peak of the tower of protestant church buildings (mainly Calvinist, but sometimes Lutheran as well) is decorated with a star polyhedron symbolizing the star of Bethlehem (or a mace or both). I would like to know whether there is something similar in other countries.

REMARK. This kind of decoration spread after 1781 when Emperor Joseph II by decree allowed protestants free practice of their religion. (Maybe the star symbol goes back to the time of anti-protestantism and religion war when this object could be considered as a weapon as well, but no intact protestant churches remained from that period, at least I do not know any evidence.) Hungarian Calvinists never put a cross on the top of their churches (they have a star or a cock), but the Lutherans do.

(b) I know that in Rome, the church Sant Ivo alla Sapienza, the dome and the facade of the church San Andrea della Valle, the dome of the Sacresty of St. Peter's catherdal, and many of the Egyptian obelisks are decorated with star polyhedra. I would like to know whether there are other exaples of star polyhedra in Rome and in other places (cities) in Italy.

REMARK. As far as I know, occurrence of star polyhedra in Rome is a consequence of the fact that many popes had stars in their coat of arms. It was a natural intention that if they wanted to represent this 2-dimensional heraldic symbol in 3-space, star polyhedra were used. Up to my knowledge, the first examples are due to Pope Sixtus V (1585-90). Many obeliscs, including that in St Peter's Square are decorated with star-polyhedron-looking objects. In fact they are not polyhedra. They are composed of two equal planar eight-pointed star polygons in a way that one is standing on a point in a vertical plane and the other is rotated by 90 degrees about the vertical axis passing through the supporting point. This object is rather a "nolid" according to Alan Holden's terminology. Later examples are real polyhedra, for instance at the church San Andrea della Valle and the obelisc in Piazza di S. Maria sopra Minerva (under Pope Alexander VII, 1655-67), the obelisk in Piazza della Rotonda (under Pope Clemens XI, 1700-21), as well as the Sacresty of St Peter's (under Pope Pius VI, 1775-99). These are elevated polyhedra, or star polyhedra with extended points.

(c) I know some church monuments in England, decorated with polyhedra: in Salisbury Cathedral, Wimbourne St Giles Parish Church, St Lowrence Church in Reading, Merton College Chapel Oxford. I know also the famous pavement mosaic attributed to P. Uccello, Basilica of St Mark in Venice, and Fra Giovanni's intarsia in the Monastery of Monte Olivetto Maggiore (near Siena) and in the church of Santa Maria in Organo, Verona. I would like to know whether there exist further polyhedra and polyhedral representations in churches.

Date: Fri, 03 Feb 2006 16:27:07 +0100
From: This email address is being protected from spambots. You need JavaScript enabled to view it.

Have been an avid on-line reader of Nexus since I visited Roncesvalles several years ago & spotted a geometrical relief on a stone in a wall there. So far as I have been able to find, there has been no discussion of this geometry, which looks like a medieval mason's work. I can see the circle geometry and guess that there is square geometry there too. What seems to be a mason's square is carved beside the geometry.


This is an isolated relief photographed carved on one of the stones in the wall of the Augustinian abbey at Roncesvalles, Navarre. The first buildings on this site are twelfth century with additions and renovations up to the 1930s. The stone on which the relief is carved and the material immediately around it appears to be similar to that used in the oldest buildings at Roncesvalles, purposely built to service the pilgrim route to Santiago. This pilgrim route is of particular interest for the fluid movement of builders and designers between France and northern Spain as Romanesque architecture developed into Gothic. Does anyone have any ideas as to what it might mean?

Date: Sat, 14 Jan 2006 16:27:07 +0100
From: This email address is being protected from spambots. You need JavaScript enabled to view it.

I have a question for the Nexus readers: "Are there any relationships between architecture and higher mathematics?" By "higher" I mean, mathematics at the level of 1st master and up. The topology paper in the NNJ vol. 7 no. 2 by Jean-Michel Kantor goes in that direction, but the reason why I propose it is different: I recently wrote a paper (in Dutch) on "Africa and higher mathematics". "True, die-hard" mathematicians sometimes take architectural math as "baby math", and of course, related to Africa, there are some down-to-earth social (extremist) influences involved. Nevertheless, in the architecture case, the question could be seen as a modification of Mario Salvadori's query at the first Nexus conference for architecture and mathematics in 1996: "Are there any relationships between architecture and mathematics?"

Date: Mon, 25 May 2009
From: Niels Bandholm - This email address is being protected from spambots. You need JavaScript enabled to view it.

Valerie Brewster Willis had a query in the Nexus Network Journal 03 Feb 2006: What is this geometrical symbol in Roncesvalles? (See figure 1)

Fig. 1

I do not have an answer but I see a similarity to a pattern I found in Keith Critchlow's book, Islamic Patterns (1976) on page 39 (see fig. 2). This figure also contains a six-pointed star and it is gyrated an angle of 19.11° from its normal position.

Fig. 2
Fig. 3


The first question: How slanted is the six-pointed star at Roncesvalles?
If the knife at left is vertical then the six-pointed star seems gyrated as in Critchlow's pattern (see fig. 3).
The second question: What is the original reference to Critchlow's pattern?
I have asked Professor Keith Critchlow and in his kind response, he is sorry not to recall the reference as the book was written in 1976.
I am extremely interested in the reference as I have a wonderful elucidation of Critchlow's pattern.

Date: Sun, 25 October 2009
From: Steve Wassell - This email address is being protected from spambots. You need JavaScript enabled to view it.

The question seems simple enough, but it quickly raises additional questions. How do we measure "major"? Do we use media coverage as a basis? Or public sentiment (and if so, how do we measure this)?
Or architectural quality and significance (and if so, how do we measure these)? In any case, I'd like to get the collective opinion of the NNJ readership. Your list can be as short or as long as you like. You can give reasons for your choices or just give a list. And just to be specific, let's agree that "of today" means the architect must be living. Can anyone come up with someone older than Oscar Niemeyer (age 101)?!