Henry Segerman
Department of Mathematics
Oklahoma State University
Stillwater, OK 74078, USA

Office: 504 Mathematical Sciences
Phone: (405) 744-7746
Email: segerman (at) math (dot) okstate (dot) edu

Curriculum Vitae


Office hours for Fall 2017: TBD.

Fall 2017: Math 2153: Calculus II.

Spring 2017: Geometry and Algorithms in Three-Dimensional Modelling, and Math 6323: Algebraic Topology.


Visualizing Mathematics with 3D Printing

Published by Johns Hopkins University Press, July 2016. This is a popular mathematics book, with the twist that most of the figures in the book are photographs of 3D printed models. These models are available for readers to download and 3D print themselves, or order online, or explore virtually on the book's website 3dprintmath.com.

Papers and preprints

Geometry and Topology

  1. Connectivity of triangulations without degree one edges under 2-3 and 3-2 moves, to appear in Proc. Amer. Math. Soc., arXiv:1605.09099, 13 pages, 14 figures.

  2. Non-geometric veering triangulations, with Craig D. Hodgson and Ahmad Issa, Experimental Mathematics 25 (2016), no. 1, pp. 17-45, 29 pages, 24 figures.

  3. Triangulations of 3-manifolds with essential edges, with Craig D. Hodgson, J. Hyam Rubinstein, and Stephan Tillmann, Annales de Mathématiques de Toulouse 24 (2015) no. 5, pp. 1103-1145, 43 pages, 14 figures.

  4. 1-efficient triangulations and the index of a cusped hyperbolic 3-manifold, with Stavros Garoufalidis, Craig D. Hodgson and J. Hyam Rubinstein, Geometry & Topology 19 (2015), pp. 2619--2689, 71 pages, 28 figures.

  5. Triangulations of hyperbolic 3-manifolds admitting strict angle structures, with Craig D. Hodgson and J. Hyam Rubinstein, Journal of Topology 5 (2012), no. 5, pp. 887-908, 22 pages, 9 figures.

  6. A generalisation of the deformation variety, Algebraic and Geometric Topology 12 (2012), no. 4, pp. 2179-2244, 66 pages, 26 figures.

  7. Pseudo-developing maps for ideal triangulations I: Essential edges and generalised hyperbolic gluing equations, with Stephan Tillmann, Topology and Geometry in Dimension Three: Triangulations, Invariants, and Geometric Structures (Proceedings of the Jacofest conference), AMS Contemporary Mathematics 560 (2011), pp. 85-102, 18 pages, 8 figures.

  8. Veering triangulations admit strict angle structures, with Craig D. Hodgson, J. Hyam Rubinstein and Stephan Tillmann, Geometry & Topology 15 (2011), pp. 2073-2089, 17 pages, 9 figures.

  9. Incompressible surfaces in handlebodies and boundary compressible 3-manifolds, with J. Nogueira, Topology and its Applications 158 (2011), no. 4, pp. 551-571, 21 pages, 14 figures.

  10. Detection of incompressible surfaces in hyperbolic punctured torus bundles, Geometriae Dedicata 150 (2011), no. 1, pp. 181-232, 52 pages, 25 figures.

  11. On spun-normal and twisted squares surfaces, Proc. Amer. Math. Soc. 137 (2009), pp. 4259-4273, 15 pages, 13 figures.

Mathematical Visualization, Art and Exposition

  1. Conformally correct tilings, with Saul Schleimer, arXiv:1612.08299 [math.HO], 6 pages, 7 compound figures.

  2. Non-euclidean virtual reality I: explorations of H3, with Vi Hart, Andrea Hawksley, and Elisabetta A. Matsumoto, Proceedings of Bridges 2017: Mathematics, Music, Art, Architecture, Culture, pp. 33-40, 8 pages, 9 figures.

  3. Non-euclidean virtual reality II: explorations of H2×E, with Vi Hart, Andrea Hawksley, and Elisabetta A. Matsumoto, Proceedings of Bridges 2017: Mathematics, Music, Art, Architecture, Culture, pp. 41-48, 8 pages, 7 figures.

  4. Magnetic sphere constructions, with Rosa Zwier, Proceedings of Bridges 2017: Mathematics, Music, Art, Architecture, Culture, pp. 79-86, 8 pages, 10 figures.

  5. Visualizing Hyperbolic Honeycombs, with Roice Nelson, Journal of Mathematics and the Arts 11 (2017), no. 1, pp. 4-39, 36 pages, many figures.

  6. Squares that Look Round: Transforming Spherical Images, with Saul Schleimer, Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Culture, pp. 15-24, 10 pages, 9 figures with many subfigures.

  7. Puzzling the 120-cell, with Saul Schleimer, Notices of the American Mathematical Society 62 (2015), no. 11, pp. 1309-1316, 8 pages, many figures. A more detailed version is available at arXiv:1310.3549 [math.GT].

  8. Hypernom: Mapping VR Headset Orientation to S3, with Vi Hart, Andrea Hawksley and Marc ten Bosch, Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture, pp. 387-390, 4 pages, 3 figures.

  9. The Quaternion Group as a Symmetry Group, with Vi Hart, Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture, pp. 143-150, 8 pages, 8 figures. This paper was republished in The Best Writing on Mathematics 2015, Princeton University Press.

  10. Triple gear, with Saul Schleimer, Proceedings of Bridges 2013: Mathematics, Music, Art, Architecture, Culture, pp. 353-360, 8 pages, 19 figures.

  11. Developing fractal curves, with Geoffrey Irving, Journal of Mathematics and the Arts 7 (2013), no. 3-4, pp. 103-121. 21 pages, 22 figures.

  12. How to print a hypercube, Math Horizons 20 (Feb 2013), issue 3, pp. 5-9, 5 pages, 9 figures.

  13. 3D printing for mathematical visualisation, Math. Intell. 34 (2012), no. 4, pp. 56-62, 7 pages, 9 figures. The final publication is available at www.springerlink.com, at this page.

  14. Sculptures in S3, with Saul Schleimer, Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture, pp. 103-110, 8 pages, 9 figures.

  15. Recent 3D printed sculptures, Hyperseeing 2011 Fall/Winter, 10 pages, 11 figures.

  16. Fractal graphs by iterated substitution, Journal of Mathematics and the Arts (© Taylor and Francis, available online at: http://www.tandfonline.com), 5 (2011), no. 2, pp. 51-70, 20 pages, 20 figures.

  17. The Sunflower Spiral and the Fibonacci metric, Proceedings of Bridges 2010: Mathematics, Music, Art, Architecture, Culture (2010), pp. 483-486, 4 pages, 4 figures.

  18. Autologlyphs, with Paul-Olivier Dehaye, 3 pages, many figures. Mathematical Intelligencer 26 (2004), no. 2, pp. 37-39, and cover art.

  19. 100 prisoners and a lightbulb, with Paul-Olivier Dehaye and Daniel Ford, Mathematical Intelligencer 25 (2003), no. 4, pp. 53-61, 9 pages, 3 figures.

My Ph.D. thesis is available here (submitted May 2007). It bears a striking resemblance to the paper "Detection of incompressible surfaces in hyperbolic punctured torus bundles".

I designed the cover art and all illustrations for the book Blast into Math! by my friend Julie Rowlett, published January 2013.


Slides and notes from some of my talks (see my CV for more):

On 23rd February 2008 I gave a talk to the University of Texas Mathematics Department's Saturday Morning Math Group (for an audience of around 200 high school students from nearby schools in the area), you can see a video of it here (scroll down to my talk).

Art Exhibitions


My YouTube channel has over 1.8 million views.

I've made guest appearances on the popular Numberphile and standupmaths channels on YouTube.


20 May 2017: James Glossop wrote on the UK Times website about a photograph he took of me at our Brilliant Geometry exhibition in Edinburgh.

21 March 2017: Davide Castelvecchi wrote an article for Nature News on my work with Vi Hart, Andrea Hawksley and Sabetta Matsumoto on non-euclidean virtual reality. The article appeared in print: Nature 543, p 473 (23 March 2017)

15 November 2016: Luke Whelan wrote an article for Wired on my work in 3D printing and virtual reality, and my book Visualizing Mathematics with 3D Printing.

June 2016: Roman Fishman (Роман Фишман) wrote a feature about my 3D printed artwork that was published in the June 2016 print edition of Popular Mechanics (Russia). The article appeared online on July 18 2016.

26 April 2016: Siobhan Roberts wrote an article for The New Yorker, on my work with Robert Fathauer and Bob Bosch on making the first injection moulded 120-sided die. Other major press included Liz Stinson writing for Wired, Holger Dambeck writing for Speigel Online, and a video by Karin Heineman for Inside Science.

1 February 2016: Evelyn Lamb wrote a blog post for the American Mathematical Society, on my investigation into editing spherical video with Möbius transformations.

14 December 2015: Gary Antonick featured a 3D animation of Saul Schleimer's and my Triple gear at the end of a New York Times Numberplay post.

15 February 2015: I gave a talk on visualising four-dimensional objects at the annual meeting of the American Association for the Advancement of Science. Science, New Scientist and NBC News wrote blog posts about it.

30 October 2014: Alex Bellos wrote a blog post for The Guardian entitled "Pumpkin geometry: stunning shadow sculptures that illuminate an ancient mathematical technique", on stereographic projection sculptures by Saul Schleimer and me.

19 May 2014: Evelyn Lamb wrote a blog post for Scientific American on "More fun than a hypercube of monkeys", a sculpture by my brother Will and me, inspired by a question of Vi Hart.

15 March 2013: Megan Gambino wrote a blog post for Smithsonian magazine on my 3D printed sculpture.

31 October 2012: Evelyn Lamb wrote a blog post for Scientific American on the "30-cell puzzle", a 3D printed puzzle by Saul Schleimer and me based on the 120-cell, one of the regular 4-dimensional polytopes.

23 August 2012: My sculpture "Dual Half 120- and 600-Cells" (joint work with Saul Schleimer) won the "Best Use of Mathematics" prize (one of four prizes awarded) at the Bridges conference 2012. It was featured in a slide show on the Scientific American website.

January 2012: I was interviewed for an article in the "Voice", a publication put out by the University of Melbourne, on "The language and art of maths". Here is the article. The online version of the article is missing the image (shown here) that went with the article. Alternatively, here is a pdf of the whole publication, which includes the article (on page 4) together with the photograph.

6 December 2011: I was interviewed by BBC Radio 5 about mathematical art and 3D printing. Here is the blogpost for the podcast. Here is the direct link to the mp3.

February 2008: I was interviewed on She Blinded Me With Science!, a show on the student radio station KVRX, talking about topology and juggling. You can listen to the interview here.


I design and produce mathematically interesting dice with Robert Fathauer, see The Dice Lab.

Images of Dehn surgery space

Go here for my personal website. Particularly math(s) related things: 3D printed sculpture, Autologlyphs, Escher's Printgallery at Stanford, Book Covers and Posters, T-shirt designs.

For keeping track of your and your friends' (lack of) mathematical progress: Ways to Go Wrong Tally Sheet.

My old University of Melbourne math website is here. My old University of Texas math website is here. My old Stanford math website is here.


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