diff --git a/src/main.rs b/src/main.rs index cc97eb6..22a3dd8 100644 --- a/src/main.rs +++ b/src/main.rs @@ -1,5 +1,6 @@ use tera::{Context, Tera}; use warp::{Filter, filters::path::Tail, Reply, Rejection}; +use warp::hyper::StatusCode; lazy_static::lazy_static! { pub static ref TEMPLATES: Tera = Tera::new("templates/**/*").expect("failed to parse templates"); @@ -27,13 +28,28 @@ async fn main() { }; warp::redirect(warp::http::Uri::from_static(target)) }); - - let routes = root.or(static_pages).or(templates); + + let routes = root.or(static_pages) + .or(templates) + .recover(handle_rejection); warp::serve(routes) .run(([0,0,0,0], 3030)) .await; } +async fn handle_rejection(err: Rejection) -> Result { + let code; + let message; + if err.is_not_found() { + code = StatusCode::NOT_FOUND; + message = std::fs::read_to_string("static/404.html").expect("/static/404.html must exist for 404 redirects"); + } else { + code = StatusCode::INTERNAL_SERVER_ERROR; + message = String::from("Internal server error"); + } + Ok(warp::reply::with_status(warp::reply::html(message), code)) +} + async fn render_template(lang: String, tail: Tail) -> Result { let mut path = format!("{lang}/{}", tail.as_str()); diff --git a/static/404.html b/static/404.html new file mode 100644 index 0000000..4f41d2a --- /dev/null +++ b/static/404.html @@ -0,0 +1,14 @@ + + + + + + 404 + + + + + +

Error 404 - The page you were looking for could not be found.

+

Click here to return to the home page.

+ diff --git a/templates/_index.html b/templates/_index.html new file mode 100644 index 0000000..0252572 --- /dev/null +++ b/templates/_index.html @@ -0,0 +1,5 @@ +{% import "common.html" as common %} +{{ common::meta(title="Spencer Whitehead - Publications") }} + + {{ common::nav() }} + diff --git a/templates/en/academic/cv/index.html b/templates/en/academic/cv/index.html deleted file mode 100644 index e531100..0000000 --- a/templates/en/academic/cv/index.html +++ /dev/null @@ -1,10 +0,0 @@ -Spencer Nicholas Whitehead's Academic Page - - -

Spencer Nicholas Whitehead

- - Research | CV | Teaching | Art -
- -

My most recent CV is available here (link to PDF; updated February 7 2023).

- diff --git a/templates/en/academic/index.html b/templates/en/academic/index.html deleted file mode 100644 index 6bc1c68..0000000 --- a/templates/en/academic/index.html +++ /dev/null @@ -1,14 +0,0 @@ -Spencer Nicholas Whitehead's Academic Page - - -

Spencer Nicholas Whitehead

-

I received my Bachelor of Mathematics and Master of Mathematics from the University of Waterloo in the years 2021 and 2022 respectively, both from the Department of Pure Mathematics. - During these degrees I worked primarily with Benoit Charbonneau in the fields of Euclidean geometry and gauge theory. - Currently I am a Ph. D. student at the Department of Mathematics at Duke University. -

- -

Aside from my research in mathematics, my primary skills are in software development and teaching. - For a complete history of my work in academia and industry, see the CV tab. - For my teaching activities, see the Teaching tab.

-

Research interests: differential geometry, Euclidean geometry, gauge theory, mathematical art

- diff --git a/templates/en/academic/teaching/2023/106/grading_info/index.html b/templates/en/academic/teaching/2023/106/grading_info/index.html deleted file mode 100644 index b640659..0000000 --- a/templates/en/academic/teaching/2023/106/grading_info/index.html +++ /dev/null @@ -1,56 +0,0 @@ -MATH 106L Grading - - - -

MATH 106L Grading - F23

-

As described in the description of grade breakdown here, grading in this offering of MATH 106L will be on a mastery grading basis. That means for each assignment, you will ultimately receive a grade of either pass or fail.

- -

In order to pass the course (graded on a pass/fail basis) you must

- -

At a glance, this seems like a lot. -Most of these bullet points specify that you must pass specific labs/worksheets at the end of the course; fundamentally, you are responsible for 27 small assignments, 6 lab reports, and 2 big assignments to pass. -All of these but the big assignments can (and should) be done in groups! This will make your life much easier.

- -

Some questions you might want to ask

- -

Did I pass assignment XYZ?

-

If ever you fail to pass an assignment, I will email you about it prior to publishing the Gradescope grades. -If you haven't received an email from me, the answer is yes!

- -

What constitutes a `pass'? — Lecture worksheets, individual lab assignments

- -

Each worksheet consists of a number of `worksheet questions' and potentially some `homework questions'. Each is worth 1 point; earning at least two thirds of the available points constitutes a pass. Your first submission will be graded for feedback only; the resubmission will be graded for correctness, and to determine whether or not a passing grade has been earned.

- -

What constitutes a `pass'? — Lab reports

- -

A lab report consists of a typed response in full sentences incorporating answers to a selection of math questions into the body of the text. -Reports will be graded on a rubric for correctness and completeness of the mathematics and quality of written presentation. (See here for best practices in writing mathematics). -A score of level 3 or higher will constitute a pass; that is, a total score of 12 or higher on the following rubric.

- - -

If your group fails to pass with a level 3 or higher on the first attempt, you will be given feedback and the opportunity to correct and make a resubmission.

- -

What constitutes a `pass'? — Big assignments

- -

The big assignments of MATH 106L are the closest thing the course has to conventional tests. -You will fill out and submit the assignment individually, and a score of 70% or higher constitutes a pass. -In the event that you fail to pass the assignment the first time, you will be given the chance to submit corrections to receive up to half of the lost points. -For example, if you earn a grade of 60% on a first submission and submit corrections for 30% of the lost marks, your final grade on the big assignment would be 60% + 1/2 x 30% = 75%; a pass.

- -

Am I on track to pass the course?

- -

Unless we've spoken and I've said something to the opposite effect, yes! If you ever don't get credit for an assignment, I will contact you about it. -You are always welcome to email me to request the records I have for grades you've earned in the course to a point.

- -

DukeHub says we have an exam on the 17th?

- -

We don't. There are no exams in this course.

- diff --git a/templates/en/academic/teaching/2023/106/index.html b/templates/en/academic/teaching/2023/106/index.html deleted file mode 100644 index 7f479cd..0000000 --- a/templates/en/academic/teaching/2023/106/index.html +++ /dev/null @@ -1,856 +0,0 @@ -MATH 106L - Fall 2023 - - - - -

MATH 106L: Lab calculus and functions II

- -

Instructor: Spencer Nicholas Whitehead

- -

Lecture times: MWF 12:00-12:50, W. Duke 08A

-

Lab times: TTh 12:00-12:50, W. Duke 08A

- -

Office Hours: W 13:00-14:00, Classroom 132; Th 16:00-17:00, F 15:00-16:00, Zoom (link sent by email). One online office hour TBD.

- -

Syllabus: See the course syllabus in PDF format here.

- -

Contact: See a facesheet of course staff and contact info in PDF format here.

- -

Grading: Detailed information on the grading scheme is available in PDF format here.

- -

A more detailed breakdown of the grading scheme and FAQ is available here.

- -

The rubric used to assess reports is available here (see above link for more grading info). - -

-Course description: The notion of quadrature, the computation of the area of a complicated shape by filling it with smaller, better understood shapes, has been studied since the Greeks. -In MATH 105L, you studied the calculus of differentials and learned how the behaviour of a (reasonable) function could be described locally by its derivative. -Historically, this notion came almost 2,000 years after that of quadrature. -It would be a further two centuries until James Gregory would publish a statement and proof of what is today known as the fundamental theorem of calculus. -This theorem states roughly that quadrature, called integration today, is inverse to differentiation: the derivative of an integral of a function is the original function, and the integral of a derivative of a function is the original function—perhaps up to the oft-forgotten '+ C'. -

-

-The fundamental theorem of calculus cannot be described as anything short of astonishing. -There is no reason a priori to believe that the operations of finding area and finding local linear approximations should be related to each other in any reasonable way, but the fundamental theorem of calculus provides exactly this relation. -The fundamental theorem of calculus comprises perhaps the first example of what one might call a 'local-global result': by knowing local information about a function (its derivative at each point), one learns global information about the function (the area under its graph). -This philosophy underlying the fundamental theorem of calculus is omnipresent in day-to-day life, if often invisible—as the sewist closes a sleeve with a stitch in the round or a ship circumnavigates the globe using only an atlas is present the fundamental theorem of calculus, providing rigorous mathematical justification to the idea that local approximations, sufficiently accurate, sum to the whole. -While often exploited as just a computational tool, it would be no exaggeration to call the fundamental theorem of calculus one of the most beautiful in all of mathematics. -

-

-In MATH 106L we will develop the modern integral calculus from a particular kind of quadrature called a Riemann sum, and from this definition prove the fundamental theorem of calculus. -After the fall break, we will begin the study of differential equations and methods of solution. -Finally, after the Thanskgiving break (and throughout the labs) we will study specific examples of differential equations that motivated the historical development of calculus, such as Newton's laws of motion and models for population growth/decay, including the presence of forcing terms. -

- -

-Best practices for writing mathematics: Through the course, you will have the chance in labs to write a number of group reports. -While there is no universal style guide for mathematical writing, there are a number of accepted best practices, available in PDF format here. -When writing reports, you are expected to follow the practices in this document. -

- -

-Textbook problems: In the interest of fairness and accessibility, I will pull practice problems and enrichment reading from the free and openly available MIT OpenCourseWare Calculus text of Strang. Click here to access this textbook. -The practice problems will be updated on a (roughly) week-by-week basis; for some weeks there may be no practice problems. -Many Duke courses use recent editions of Hughes-Hallett; this is a resource you may consider purchasing or finding in the library, but is not required for this class. -My personal favourite calculus texts are those of Michael Spivak. -I highly recommend them for enrichment reading, but again do not require them for this class. -See the syllabus for more information on titles, editions, etc. -

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
LessonDateTopicWorksheetDue DateResourcesTextbook practice
(Not to hand in)		External resources
1-12023-08-28105L ReviewWorksheet2023-09-04
Lab2023-08-29Trigonometry, ILab 12023-09-04Section 1.5Basic trig
1-22023-08-30Trigonometry, IIWorksheet2023-09-04Unit circle
Radians
Lab2023-08-31Trigonometric
modelling, I		Lab 2Spreadsheet
Geogebra		Section 1.5Sinusoidal models
1-32023-09-01Trigonometric
identities, limits		Worksheet2023-09-04Section 1.5Trig identities
Angle addition
2023-09-04Labour day, no class
Lab2023-09-05Trigonometric
modelling, II		Report: Global
warming [group]		2023-09-13Section 1.5
2-22023-09-06Trigonometric
Derivatives		Worksheet2023-09-11Section 2.4Differentiating trig functions
Lab2023-09-07Newton's laws
of motion, I		Lab 3
2-32023-09-08Inverse trigonometric
functions 		Worksheet2023-09-11Inverse trig functions
3-12023-09-11Trigonometric
inverse derivatives		Worksheet2023-09-18The inverse function theorem
Lab2023-09-12NO LABBIG ASSIGNMENT 12023-09-22
3-22023-09-13Trigonometric
related rates		Worksheet2023-09-18
Lab2023-09-14Newton's laws
of motion, II		Group report: understanding gravity2023-09-20
3-32023-09-15Postition, velocity,
Acceleration		Worksheet2023-09-18
4-12023-09-18Distance from velocityWorksheet2023-09-25
Lab2023-09-19Sums, sigma notation
4-22023-09-20Left- and right-
handed sums		Worksheet2023-09-25
Lab2023-09-21Sums and sigma notation, IILab questions [individual]2023-09-27
4-32023-09-22The definite integralWorksheet2023-09-25
5-12023-09-25Midpoint and
trapezoid sums		Worksheet2023-10-02
Lab2023-09-26Postponed due to technical issues
5-22023-09-27FTC IWorksheet2023-10-02A proof of FTC in an easy case
Lab2023-09-28Riemann sums, ISpreadsheet
5-32023-09-29FTC I, cont.See 5-2
6-12023-10-02Properties of definite
integrals		Worksheet2023-10-09
Lab2023-10-03Riemann sums, II
6-22023-10-04Constructing
antiderivatives		Worksheet2023-10-09
Lab2023-10-05Riemannian Sums, IIIGroup report2023-10-11
6-32023-10-06Integration by substitutionWorksheet2023-10-09
7-12023-10-09Integration by partsWorksheet2023-10-23
Lab2023-10-10Average value of
a function, I
7-22023-10-11Antidifferentiation
practice, I		Worksheet2023-10-23
Lab2023-10-12Average value of a function, IIGroup report2023-10-18Also note:BIG ASSIGNMENT 22023-10-27
2023-10-13Fall break, no class
2023-10-16Fall break, no class
2023-10-17Fall break, no class
8-22023-10-18Antidifferentiation
practice, II		See 7-2
Lab2023-10-19Average Values, II
8-32023-10-20Integrating to infinityWorksheet2023-10-23
9-12023-10-23Other improper integralsWorksheet2023-10-30
Lab2023-10-24NO LAB
9-22023-10-25Big assignment help
Lab2023-10-26Force and Work: I
9-32023-10-27FTC IIWorksheet2023-10-30
10-12023-10-30Differential equations,
initial value problems, I		Worksheet2023-11-06
Lab2023-10-31Force and Work: II2023-11-08
10-22023-11-01Differential equations,
initial value problems, II
Lab2023-11-02Differential equations, I
10-32023-11-03Slope fields, equilibria, IWorksheet2023-11-06
11-12023-11-06Slope fields, equilibria, II
Lab2023-11-07Differential equations, IIReport: Short report [group]2023-11-15
11-22023-11-08Separation of variables, IWorksheet2023-11-13
Lab2023-11-09Euler's methodSpreadsheet
11-32023-11-10Separation of variables, II
12-12023-11-13Growth and decayWorksheet2023-11-20
Lab2023-11-14Euler's methodReport: Short report [group]2023-11-22
12-22023-11-15Applications: heating
and mixing, I		Worksheet2023-11-20
Lab2023-11-16Euler's methodBIG ASSIGNMENT 32023-11-27
12-32023-11-17Applications: heating
and mixing, I cont.
13-12023-11-20Applications: heating
and mixing, II (online only)		Worksheet2023-11-27
2023-11-21Thanksgiving, no class
2023-11-22Thanksgiving, no class
2023-11-23Thanksgiving, no class
2023-11-24Thanksgiving, no class
14-12023-11-27Worksheet2023-12-04
Lab2023-11-28Chemical rates
14-22023-11-29The logistic model for
population, I
Lab2023-11-30
14-32023-12-01The logistic model for
population, II		Worksheet2023-12-04
15-12023-12-04Population models
with migration		Worksheet
Lab2023-12-05Logistic model:
fishing
15-22023-12-06Applications of the
logistic model
Lab2023-12-07Logistic model:
fishing		Report: Short report [group]2023-12-15
15-32023-12-08Course evaluations
- - diff --git a/templates/en/academic/teaching/index.html b/templates/en/academic/teaching/index.html deleted file mode 100644 index a958bb5..0000000 --- a/templates/en/academic/teaching/index.html +++ /dev/null @@ -1,83 +0,0 @@ -Spencer Nicholas Whitehead's Academic Page - - -

Spencer Nicholas Whitehead

- - Research | CV | Teaching | Art -
- -

For the Fall 2023 semester I am instructor of record on MATH 106L. Click here to access the course webpage for MATH 106L.

-

Below are a list of my previous teaching activities.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
RoleCourseTermInstitution
Lab TAMATH 111
Calculus 1		Fall 2022Duke
MarkerPMATH 347
Intro to Groups and Rings		Spring 2022Waterloo
MarkerPMATH 365
Differential Geometry		Winter 2022Waterloo
TAMATH 137
Calculus 1 for Hon. Math		Fall 2021Waterloo
Tutor
(Official)		MATH 136
Lin. Alg. 1 for Hon. Math		Winter 2021Waterloo
TA leadMATH 135
Algebra for Hon. Math		Fall 2020Waterloo
Tutor
(Official)		MATH 136Fall 2019Waterloo
Tutorial lecturerCS 246
Obj. Oriented Soft. Devel		Fall 2019Waterloo
Tutorial lecturerCS 246Winter 2018Waterloo
Instructional
support (full-time)		CS 246Fall 2018Waterloo
- diff --git a/templates/en/homelab/index.html b/templates/en/homelab/index.html new file mode 100644 index 0000000..7f8e97e --- /dev/null +++ b/templates/en/homelab/index.html @@ -0,0 +1,23 @@ +{% import "common.html" as common %} +{{ common::meta(title="Spencer Whitehead - Homelab") }} + + {{ common::nav() }} +

Homelab

+ The website you are currently viewing is being served by my personal computing homelab, a cluster of three nodes orchestrated by k3s. + +

crusader

+ crusader is a VPS managed by Vultr, used as a secure reverse proxy to my primary nodes. + It is responsible for running a Nginx proxy server. + +

churchill

+ churchill was built in 2014, featuring an AMD FX-8310 chip and 8GB of RAM, running Devuan Linux 6. + It is the control node for the k3s cluster, and is responsible for lightweight web services such as this website and my private git server. + +

valentine

+ valentine was built in 2018. It has a AMD Ryzen 7 1700 chip and 16GB of DDR4 2400 RAM, running Linux Mint 21. + It is responsible for heavier media services, such as Jellyfin and Subsonic. + +

blackprince

+ blackprince was built in 2025. It has an AMD Ryzen 7 7700XD chip, an Nvidia GeForce 1080 GPU, and 64GB of DDR5 3200 RAM, running Linux Mint 22. + It is primarily used as a personal computing node, and for running more intense computations for research purposes. + diff --git a/templates/en/index.html b/templates/en/index.html index 85ad546..57bed0a 100644 --- a/templates/en/index.html +++ b/templates/en/index.html @@ -5,4 +5,6 @@

This is the personal website of Spencer Whitehead. I am a fourth-year Ph.D. candidate at Duke University, expecting to graduate in early 2027. My primary research interests are in gauge theory, four- and eight-dimensional differential geometry, and the applications of computer algebra systems to solving problems in geometry.

Resume

+

Publications

+

Homelab

diff --git a/templates/en/publications/index.html b/templates/en/publications/index.html new file mode 100644 index 0000000..53a76d4 --- /dev/null +++ b/templates/en/publications/index.html @@ -0,0 +1,42 @@ +{% import "common.html" as common %} +{{ common::meta(title="Spencer Whitehead - Publications") }} + + {{ common::nav() }} +

Publications

+

This page contains a list of my published (scholarly) works with plain-language descriptions of the results.

+
+

On a smoothness characterization for good moduli spaces, joint with Dan Edidin and Matt Satriano, published in Advances in Mathematics in April 2024.

+

A preprint is available for free on the arXiv. I was responsible for writing the second section of this paper (pp. 5 - 20 in the preprint).

+

In mathematics, we are often interested in the spaces that result when taking a large space and 'identifying' some points (making a new, smaller space by declaring some points to be indistinguishable from each other). A typical example would be folding a piece of paper in half: so the top left corner is identified with the bottom left corner, and so on. Identifications that arise from a procedure like folding a sheet of paper leave a crease in the paper, points that are not identified to any other point. Mathematicians call such points singular (meaning 'exceptional/rare'), as the crease line is a one-dimensional object, while the paper itself is two-dimensional. The opposite of singular is smooth.

+ +

We considered the general problem of identifying which paper-folding rules were singular, and which were smooth (in mathematical jargon: which complex representations of a group have smooth GIT quotients?) The answer for a list of finitely many rules has been known since the 1950s, due to Shephard and Todd—the space is smooth only when the rules are generated by those rotating one dimension and leaving fixed a hyperplane. + In our work, we allow for infinitely many rules, and recovered in some cases a natural generalization of the theorem of Shephard and Todd: we prove roughly that smoothness follows when the rules are generated by a rotation in one dimension leaving fixed a hypersurface.

+
+ +
+

Generalized Pythagorean Lutes, published in the Proceedings of Bridges 2022 in August 2022.

+

The paper is available for free from the proceedings here (PDF, 8MB).

+ +

In this paper I investigated the construction of a geometric pattern (attributed to Pythagoras, but probably much more recent) called the "lute of Pythagoras". The pattern features an appealing self-symmetry between the pentagon and its stellation, the pentagram, demonstrating how they fit 'within' each other in an infinite chain, descending in scale exponentially with the golden ratio. In this short paper, I formalized the geometric structure of the lute of Pythagoras and generalized it to higher dimensions. I proved that such structures can exist only in dimensions 2, 3, and 4, and that the lute of Pythagoras itself is a two-dimensional shadow of a larger 'generalized lute of Pythagoras' existing in four dimensions, based on an exceptional four-dimensional shape called the dodecaplex.

+
+ +
+

Integrality theorems for symmetric instantons, M.Math thesis (supervised by Benoit Charbonneau), August 2022.

+

This thesis is available online through UWSpace.

+ +

In this thesis, I studied objects from mathematical physics called 'instantons': particular solutions to the Yang—Mills equations that appear in various places in geometry, topology, knot theory, and high-energy particle physics. The instanton equations are very complicated, and thus difficult to solve directly. One promising idea is to look just for solutions that have some prescribed symmetry; these symmetries impose additional equations that can in some cases be used to directly construct interesting examples of instantons.

+ +

The original methodology for constructing instantons by symmetries was set out in a series of papers by Singer, Sutcliffe, et al. from the late 1990s and early 2000s. In my thesis, I generalized their framework and provided a formal proof of correctness. Then, I used the generalized framework to resolve a series of questions that had been left open in the original papers, constructing two new examples of instantons with the symmetries of the dodecahedron, and using a computer to prove that any instanton with the symmetries of a dodecaplex must satisfy a certain lower bound on its charge, resolving a 2013 question of Allen—Sutcliffe.

+
+ +
+

Studying Wythoff and Zometool constructions using Maple, joint with Benoit Charbonneau, published in Maple in Mathematics Education and Research in February 2020.

+

A preprint is available for free on the arXiv. I was responsible for the initial writing of the paper and most of the software development.

+ +

In this paper, we concern ourselves with the mathematical educational toy Zometool. We had experience working in large-scale projects with Zometool previously (see the Great Omnitruncated Dodecaplex Barn Raising Project, University of Waterloo 2019), in which we built certain four-dimensional geometric objects using Zometool.

+ +

Any time one builds a four-dimensional object in three-dimensions, it is necessary to "project a dimension away": for example, by placing the skeleton of a three-dimensional cube in front of a light source, one can project it to a two-dimensional image on a wall. + Not all projections are equal: some (like the stereographic projection distort lengths, while others (such as the orthogonal projection, where we imagine an infinitely strong light source placed infinitely far away) may cause edges to cross each other. In this project, we created a software package in Maple to determine what projections could actually be constructed in the Zometool building system, and to generate plans for building complicated geometric projections in Zometool. We focused especially on a class of shapes called Wythoff constructions, which are the result of looking at images of a point in a system of mirrors called a kaleidoscope.

+
+ +