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Discrete Geometry Lab
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The lab explores the properties of convex polytopes through geometry and combinatorics.
AboutAbout the lab
Exploring convex polytopes through geometry and combinatorics
The Discrete Geometry Lab studies the properties of convex polytopes from both geometric and combinatorial perspectives.
Commutative rings associated with convex polytopes are also a subject of study.
Through this research and education, the lab also aims at applications in information science.
The lab's faculty describe their research topic as algebraic combinatorics.
Key terms
- Convex polytope
- A solid bounded by flat faces in which the line segment joining any two points inside never leaves the solid. A cube is an example.
- Combinatorics
- A field of mathematics that studies the rules for counting, arranging, and combining objects.
- Commutative ring
- A set in which you can add, subtract, and multiply, and where changing the order of multiplication does not change the result. The integers are an example.
ResearchResearch themes
This lab investigates the geometric and combinatorial properties of convex polytopes. It also studies commutative rings associated with convex polytopes, and aims at applications in information science.
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MembersFaculty
- Associate ProfessorAkihiro Higashitani
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Stereographic polytope 24cell” Fritz.obermeyer at English Wikipedia / Public domain (cropped)
- Geometry and Combinatorics of Convex Polytopes: “Stereographic polytope 16cell” Fritz.obermeyer at English Wikipedia / Public domain (cropped)
- Related lab (離散構造学講座): “Symmetries ( )” P K / CC BY 2.0 (cropped)
- Related lab (大規模数理学講座): “Contours in the vector field f(z) = -Cos(z)” Oldtimermath / CC BY-SA 3.0 (cropped)
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