About: Jessen's icosahedron

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Jessen's icosahedron, sometimes called Jessen's orthogonal icosahedron, is a non-convex polyhedron with the same numbers of vertices, edges, and faces as the regular icosahedron. It is named for Børge Jessen, who studied it in 1967. In 1971, a family of nonconvex polyhedra including this shape was independently discovered and studied by Adrien Douady under the name six-beaked shaddock; later authors have applied variants of this name more specifically to Jessen's icosahedron.

Attributes	Values
rdfs:label	Jessen's icosahedron (en) Icosaèdre de Jessen (fr) Икосаэдр Йессена (ru) 耶森二十面體 (zh)
rdfs:comment	L'icosaèdre de Jessen (parfois appelé icosaèdre orthogonal de Jessen) est un polyèdre non convexe ayant le même nombre de sommets, d'arêtes et de faces que l'icosaèdre régulier, et dont les faces se coupent à angle droit ; il a été étudié par (en) en 1967. (fr) Икосаэдр Йессена — тип невыпуклого многогранника, построенный Йессеном в 1967 году. (ru) 耶森二十面體又稱為耶森正交二十面體是一種，其具有與正二十面體相同的面數、邊數和頂點數，拓樸結構上對應的圖亦相同。耶森二十面體的名稱來自1967年研究此種立體的，然而在伯格·耶森發表關於此種立體的研究之前就建造了此種立體的模型。耶森二十面體的面只能以直角相交，然而其無法全部的面都與座標軸平行。耶森二十面體是一種不穩定的多面體，雖然其不是彈性多面體但其仍然保留了些許可動性。若用竿子和繩子沿這種立體的邊緣搭建出一個立體結構，則這個立體結構是一種常見的张拉整体結構，稱為六杆张拉整体结构、张拉整体二十面體或擴展八面體。 (zh) Jessen's icosahedron, sometimes called Jessen's orthogonal icosahedron, is a non-convex polyhedron with the same numbers of vertices, edges, and faces as the regular icosahedron. It is named for Børge Jessen, who studied it in 1967. In 1971, a family of nonconvex polyhedra including this shape was independently discovered and studied by Adrien Douady under the name six-beaked shaddock; later authors have applied variants of this name more specifically to Jessen's icosahedron. (en)
name	Jessen's icosahedron (en)
foaf:depiction
dcterms:subject	Nonconvex polyhedra
Wikipage page ID	20347079 (xsd:integer)
Wikipage revision ID	1087835868 (xsd:integer)
Link from a Wikipage to another Wikipage	Cartesian coordinate system NASA Institute for Advanced Concepts Rational variety Dehn invariant Cuboctahedron University of Twente Polyhedron Jitterbug transformation Equilateral triangle Convex hull Convex position Order of approximation Regular octahedron Complete variety Buckminster Fuller Børge Jessen Adrien Douady Algebraic geometry Algebraic variety Cyclic permutation Nonconvex polyhedra Dihedral symmetry in three dimensions Hilbert's third problem Isogonal figure Isosceles triangle Projective variety Right angle Structural rigidity Counterexample Tensegrity Tetrahedron Triangulation (geometry) Dihedral angle Convex polyhedron H. S. M. Coxeter Icosahedron Michel Demazure Vertex (geometry) Flexible polyhedron Schönhardt polyhedron Smooth scheme Star domain dbr:File:Jessen_icosahedron.stl
Link from a Wikipage to an external page	http://www.polyhedra-world.nc/Jessen_.htm
sameAs	Jessen's icosahedron Jessen's icosahedron Jessen's icosahedron Jessen's icosahedron Jessen's icosahedron Jessen's icosahedron
dbp:wikiPageUsesTemplate	dbt:CSS_image_crop dbt:Commons_category dbt:Em dbt:Good_article dbt:Ill dbt:Multiple_image dbt:R dbt:Reflist dbt:Short_description dbt:Infobox_polyhedron
thumbnail	wiki-commons:Special:FilePath/Jessen's_icosahedron.svg?width=300
net	Jessen icosahedron net.svg (en)
bSize	400 (xsd:integer)
caption	Distances between selected points (en) View with translucent faces (en)
cHeight	275 (xsd:integer)
cWidth	275 (xsd:integer)
description	, a tensegrity sculpture whose struts and cables form the outline of Jessen's icosahedron, at the University of Twente (en)
edges	6 (xsd:integer) 24 (xsd:integer) (en)
image	Jessen's icosahedron with dimensions.png (en) Translucent Jessen icosahedron.svg (en)
oLeft	50 (xsd:integer)
oTop	10 (xsd:integer)
properties	Isogonal figure (en) not infinitesimally rigid (en)
total width	480 (xsd:integer)
vertices	12 (xsd:integer)
has abstract	Jessen's icosahedron, sometimes called Jessen's orthogonal icosahedron, is a non-convex polyhedron with the same numbers of vertices, edges, and faces as the regular icosahedron. It is named for Børge Jessen, who studied it in 1967. In 1971, a family of nonconvex polyhedra including this shape was independently discovered and studied by Adrien Douady under the name six-beaked shaddock; later authors have applied variants of this name more specifically to Jessen's icosahedron. The faces of Jessen's icosahedron meet only in right angles, even though it has no orientation where they are all parallel to the coordinate planes. It is a "shaky polyhedron", meaning that (like a flexible polyhedron) it is not infinitesimally rigid. Outlining the edges of this polyhedron with struts and cables produces a widely-used tensegrity structure, also called the six-bar tensegrity, tensegrity icosahedron, or expanded octahedron. (en)

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