Asymmetric constraints with polyhedral sets in MPC with application to coupled tanks system by Kouvaritakis, B, Cannon, M, Karas, A, Rohal-Ilkiv, B, Belavy, C, IEEE, IEEE

“…The work here adopts low complexity polyhedra for which invariance and feasibility under asymmetric constraints can be handled through the use of Farkas' lemma and related results. …”

RbEr₂AsS₇: A Rubidium-Containing Erbium Sulfide Thioarsenate(III) with (S₂)²⁻ Ligands According to RbEr₂S(S₂)[AsS<... by Katja Engel, Thomas Schleid

“…The [ErS₉] polyhedra are corner- and face-connected, while the [ErS₇] units share common edges, both building chains along [010]. …”
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An ambient-temperature stable nanoparticle-based vaccine for nasal application that confers long-lasting immunogenicity to carried antigens by Adolfo Cruz-Resendiz, Adolfo Cruz-Resendiz, Gonzalo Acero, Alicia Sampieri, Goar Gevorkian, Carolina Salvador, Laura Escobar, Margarita Jacaranda Rosendo-Pineda, Mara Medeiros, Luis Vaca

“…Polyhedrins are viral proteins present in a large family of baculoviruses that form occlusion bodies (polyhedra). These structures protect the virus particles from the outside environment until they are ingested by susceptible insects. …”
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Three-Dimensional Flight Corridor: An Occupancy Checking Process for Unmanned Aerial Vehicle Motion Planning inside Confined Spaces by Sherif Mostafa, Alejandro Ramirez-Serrano

“…This corridor is formulated as a series of interconnected overlapping convex polyhedra bounded by the perceived environmental geometries, which facilitates the generation of suitable 3D flight paths/trajectories that avoid local minima within the corridor boundaries. …”
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Methods to program and to probe RNA tertiary structure with nucleic acid origami by Parsons, Molly F.

“…The resulting algorithm for designing RNA-scaffolded polyhedra enables precise, covalent anchoring of a target RNA fragment onto a wireframe polyhedra. …”
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The Gomory-Chvátal closure : polyhedrality, complexity, and extensions by Dunkel, Juliane

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Icosadeltahedral Geometry of Geodesic Domes, Fullerenes and Viruses: A Tutorial on the T-Number by Antonio Šiber

“…The underlying symmetry of all structures is explained and thoroughly visually represented. Euler’s theorem on polyhedra is used to calculate the number of vertices, edges, and faces in domes, number of atoms, bonds, and pentagonal and hexagonal rings in fullerenes, and number of proteins and protein–protein contacts in viruses. …”
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Critically-Finite Dynamics on the Icosahedron by Scott Crass

“…The present article shows how to build such &#8220;dynamical polyhedra&#8221; for other icosahedral maps. First, algebra associated with the icosahedron determines a special family of maps with 60 periodic critical points. …”
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DC-Programming versus ℓ0-Superiorization for Discrete Tomography by Gibali Aviv, Petra Stefania

“…We show that ℓ0-minimization over bounded polyhedra can be equivalently formulated as a DC program. …”
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An Application of Line-labeling and other Scene-analysis Techniques to the Problem of Hidden-line Removal by Lavin, Mark A.

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A Polyhedral Intersection Theorem for Capacitated Spanning Trees by Hall, Leslie A., Magnanti, Thomas L.

“…This result is one of very few known cases in which the intersection of two integer polyhedra yields another integer polyhedron. We also give a complete polyhedral characterization of a related polytope, the 2-capacitated forest polytope.…”
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Recognition and Localization of Overlapping Parts from Sparse Data by Grimson, W. Eric L., Lozano-Perez, Tomas

“…The objects are modeled as polyhedra (or polygons) having up to six degreed of positional freedom relative to the sensors. …”
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Asymmetric constraints with polytopic sets in MPC with application to coupled tanks system by Kouvaritakis, B, Cannon, M, Karas, A, Rohal-Ilkiv, B, Belavy, C

“…The work here adopts low-complexity polyhedra for which invariance and feasibility under asymmetric constraints can be handled through the use of Farkas' lemma and related results. …”

Distinctive representations for the recognition of curved surfaces using outlines and markings by Forsyth, D, Zisserman, A, Malik, J

“…In such special cases as polyhedra, surfaces of revolution, general cones, canal surfaces and algebraic surfaces, the geometry can be recovered with varying degrees of success and of ambiguity. …”

Three-dimensional preservation of a non-biomineralized arthropod in concretions in Silurian volcaniclastic rocks from Herefordshire, England by Orr, P, Briggs, D, Siveter, D, Siveter, D

“…Specimens are preserved in calcite that co-precipitated with framboids and polyhedra of pyrite. The texture of the calcite indicates that it is a void infill. …”

On the Connectedness of the Moduli Space of Calabi--Yau Manifolds by Avram, A, Candelas, P, Jancic, D, Mandelberg, M

“…This is achieved by exploiting techniques of toric geometry and the construction of Batyrev that relate Calabi-Yau manifolds to reflexive polyhedra. Taken together with the previously known fact that the moduli space of all CICY's is connected, and is moreover connected to the moduli space of the present class of Calabi-Yau manifolds (since the quintic threefold P_4[5] is both CICY and a hypersurface in a weighted P_4, this strongly suggests that the moduli space of all simply connected Calabi-Yau manifolds is connected. …”

TOF-2: a large 1D channel thorium organic framework. by Ok, K, Sung, J, Hu, G, Jacobs, R, O'Hare, D

“…TOF-2 exhibits a hexagonal channel structure consisting of eight-coordinate ThO6F2 polyhedra and 1,3,5-benzentricarboxylate ligands. The channels run along the c-axis and are approximately 13 A in diameter. …”

Combinatorial structures in online and convex optimization by Gupta, Swati, Ph. D. Massachusetts Institute of Technology

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Characterization of Granulovirus and Nucleopolyhedrovirus Isolated from Spodoptera Litura by Lau, Wei Hong

“…Two baculoviruses were isolated and identified from Spodoptera litura; S. litura nucleopolyhedrovirus (SpltNPV) and S. litura granulovirus (SpltGV). The polyhedra of SpltNPV were about 0.9-1.83 µm in diameter containing multiple virions measuring about 100-280 nm wide and 320-410 nm long. …”
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Continuous Flattening of a Regular Tetrahedron with Explicit Mappings by Jin-ichi Itoh, Chie Nara

“…<p>We proved in [10] that each Platonic polyhedron<em> P</em> can be folded into a flat multilayered face of <em>P</em> by a continuous folding process of polyhedra. In this paper, we give explicit formulas of continuous functions for such a continuous flattening process in R<span style="line-height: 150%; font-family: 'Calibri','sans-serif'; font-size: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: RU; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;">³</span> for a regular tetrahedron.…”
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