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	The Polyhedra of M.C. Escher
		Stars, wood engraving, 1948, illustrated below, features the compound of three octahedra, a compound of two cubes, and the stella octangula, all in both outline and solid form, along with dozens of other polyhedra.
		Double Planetoid, wood engraving, 1949, is based on the stella octangula.
		stella octangula (compound of two tetrahedra), (both a solid and an edge model)
	www.georgehart.com /virtual-polyhedra/escher.html (436 words)

	polyhedral compound (Site not responding. Last check: 2007-10-13)
		A polyhedral compound is a polyhedron which is itself composed of several other polyhedra sharing a common centre, the three-dimensional analogs of polygonal compounds such as the hexagram.
		The best known is the compound of two tetrahedra called the stella octangula, discovered by Kepler.
		The stella octangula can also be regarded as a compound of a tetrahedron with its dual polyhedron, inscribed in a common sphere so that the vertices of one line up with the face centres of the other.
	www.yourencyclopedia.net /polyhedral_compound.html (259 words)

	Polyhedral compound -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-13)
		The best known is the compound of two (additional info and facts about tetrahedra) tetrahedra called the stella octangula, discovered by (German astronomer who first stated laws of planetary motion (1571-1630)) Kepler.
		The vertices of the two tetrahedra define a (A block in the (approximate) shape of a cube) cube and the intersection of the two an (Any polyhedron having eight plane faces) octahedron, which shares the same face-planes as the compound.
		The stella octangula can also be regarded as a compound of a tetrahedron with its (additional info and facts about dual polyhedron) dual polyhedron, inscribed in a common (A particular environment or walk of life) sphere so that the vertices of one line up with the face centres of the other.
	www.absoluteastronomy.com /encyclopedia/p/po/polyhedral_compound.htm (301 words)

	Polyhedral compound - Wikipedia, the free encyclopedia
		The best known is the compound of two tetrahedra called the stella octangula, a name given to it by Kepler.
		The vertices of the two tetrahedra define a cube and the intersection of the two an octahedron, which shares the same face-planes as the compound.
		Each of the tetrahedral compounds is self-dual, and the compound of 5 cubes is dual to the compound of 5 octahedra.
	en.wikipedia.org /wiki/Polyhedral_compound (240 words)

	Polyhedral compound (Site not responding. Last check: 2007-10-13)
		A polyhedral compound is a polyhedron which is itself composed of several polyhedra sharing a common centre the three-dimensional of polygonal compounds such as the hexagram.
		The best known is the compound of tetrahedra called the stella octangula discovered by Kepler.
		The stella octangula can also be regarded a compound of a tetrahedron with its dual polyhedron inscribed in a common sphere so that the vertices of one up with the face centres of the The corresponding cube-octahedron and dodecahedron-icosahedron compounds are first stellations of the cuboctahedron and icosidodecahedron respectively.
	www.freeglossary.com /Polyhedral_compound (316 words)

	Polyhedral compound (Site not responding. Last check: 2007-10-13)
		A polyhedral compound is a polyhedron which is itselfcomposed of several other polyhedra sharing a common centre, the three-dimensional analogs of polygonal compounds such asthe hexagram.
		The vertices of the two tetrahedra define a cube and the intersection of the two an octahedron,which shares the same face-planes as the compound.
		The stella octangula can also be regarded as a compound of a tetrahedron with its dual polyhedron, inscribed in a common sphere so that thevertices of one line up with the face centres of the other.
	www.therfcc.org /polyhedral-compound-177446.html (204 words)

	Math Forum: Orlando Meetings: Presentation Summary (Site not responding. Last check: 2007-10-13)
		The stella octangula is a star-like solid whose faces are equilateral triangles.
		Each student built a stella octangula by gluing a small tetrahedron onto each face of the large one, matching one faces of the small tetrahedron with the center triangles (obtained from dividing each face of the large tetrahedron into 4 small equilateral triangles) on the large tetrahedron.
		By fitting a stella octangula into a cube, students can identify each rotation of a cube with a permutation of four vertices of one tetrahedron out of a stella octangula.
	www.mathforum.org /orlando/kim.orlando.html (221 words)

	facetting diagrams (Site not responding. Last check: 2007-10-13)
		The regular compound of two tetrahedra, or stella octangula, is a well-known facetting of the cube.
		Sides a are sections of the square faces of the original cube and b are of the triangular faces of the stella octangula.
		Points M section the edges of the cube and N those of the stella octangula, which are also the diagonals of the original square faces.
	www.queenhill.demon.co.uk /polyhedra/FacetingDiagrams/FacetingDiags.htm (2090 words)

	Geometry Forum - CES 1995 Summer Institute - Stella Octangula
		The first group explored the construction of the stella octangula (a stellated octahedron).
		The third group played with color schemes on models of the stella octangula.
		The last group explored the relationship between the volumes of a full stella, its parts, and a cube, using three mirrors.
	www.mathforum.org /ces95/ces95.stella.html (527 words)

	From a Plane to Stella Octangula
		We consider it as compound polyhedron as it is composed of a tetrahedron and its reciprocal (a second Tetrahedron rotated 180° with respect to the first).
		The stella octangula is also called a stellated tetrahedron.
		Stella octangula is a well known in mathematics polyhedron and it was discovered in 1609 by famous German astronomer and mathematician Johannes Kepler.
	www.interklasa.pl /pabich/eng1.htm (554 words)

	Cecilia Cotton - Stella Octangula
		My most recent origami creation is this stella octangula or stellated tetrahedron.
		There are no instructions on the page for making the stella octangula although there is a picture of the finished product.
		To make the stella octangula they all must have the same parity though.
	www.ceciliacotton.ca /archives/00000185.htm (155 words)

	Geometry Forum - CES 1995 Summer Institute - Stella Octangula
		The first group explored the construction of the stella octangula (a stellated octahedron).
		The last group explored the relationship between the volumes of a full stella, its parts, and a cube, using three mirrors.
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	mathforum.org /ces95/ces95.stella.html (542 words)

	The Renaissance Man's Polyhedra Weeb Site: Polyhedron Models for the Classroom by Magnus J. Wenninger
		This is the eight-pointed star—or stella octangula, as Kepler called it—which actually turns out to be a compound of two tetrahedra— It is even more interesting to find among the stellations of the icosahedron other compounds; but more about these later.
		None of these compounds is classified with the uniform polyhedra, precisely because they are compounds; specifically, they are intersecting polyhedra or interpenetrating polyhedra, not intersecting polygons.
		To make a model of the stella octangula, all you need for a net is an equilateral triangle.
	www.theweebsite.com /polyhedra/pmftc/pmftc5.html (1150 words)

	Pyramorphix
		A related puzzle is the Stern, a German puzzle made in the early eighties.
		It is in the shape of a Stella Octangula - the pyramorphix would be obtained from this if four of its corners (the ones that only have one colour) are flattened.
		You now have two new puzzles, an octahedron and a Stella Octangula.
	www.geocities.com /jaapsch/puzzles/pyramorf.htm (1647 words)

	Transforming a tetrahedron into a fractal cube (Site not responding. Last check: 2007-10-13)
		The idea was to start with a Platonian solid, for example a tetrahedron, and then in a symmetric manner adding on its faces other tetrahedrons as shown in the four pictures above.
		In this way the first stellated form of the tetrahedron becomes Kepler's stella octangula.
		By (infinitely) repeating this process a series of non-convex polyhedra are generated (all made of identical equilateral triangles) which converge towards what may be called a "fractal cube", i.e., a solid with a fractal surface area.
	www.ux.his.no /~ruoff/FractalCube.html (209 words)

	The Stella Octangula
		This book contains 79 pages of flline masters that guide students in learning about the Stella Octangula.
		This book includes instructions for 12 independent student projects, an annotated bibliography, and flline masters for creating the models.
		Teacher's pages provide answers and extensive comments that help extend classroom discussions, relate topics to each other, and connect the stella octangula to other curriculum topics.
	www.mathteacherstore.com /middle/midlbook/5-8mathbook/titles/170181main.htm (107 words)

	Stella Octangula Video - - Christianbook.com
		The Stella Octangula, created for students in dazzling computer animation, presents three views of this intriguing stellated octahedron that illustrate some of its surprising properties.
		The video can be used by itself or shown to students working with The Stella Octangula Activity Book.
		Using The Stella Octangula Materials offers teachers background mathematics and shows how the activities and manipulatives can be used in the classroom.
	www.christianbook.com /Christian/Books/product?item_no=553041 (149 words)

	Quasitruncated Cuboctahedron (Site not responding. Last check: 2007-10-13)
		The amazing thing about this model is that it has an intrigate interior structure formed by the 8 hexagons.
		The interior structure consists of an octahedron and a stella octangula, where the octahedron is the base for the stella octangula.
		In the model one can look into one of those through the triangular hole that was formed by this process of cutting off one vertex of the stella octangula.
	www.tum.dds.nl /polyh/qtco.htm (557 words)

	Amazon.com: "stella octangula": Key Phrase page (Site not responding. Last check: 2007-10-13)
		See all pages with references to "stella octangula".
		(To have your stella octangula stand up on a point, place three r1s into one vertex, forming a tripod stand.) Q3 Visualize the shape that...
		Names like stella octangula and rhombic dodecahedron may sound a bit complicated, but they are descriptive and, once you know them, you find...
	www.amazon.com /phrase/stella-octangula (350 words)

	Solutions 5
		The stella octangula has 24 faces, 8 vertices with 3 incident edges and 6 vertices with 8 incident edges.
		Hence the symmetry groups of the stella octangular are the same as those of the cube/octahedron.
		Colouring the upper and lower faces or edges of the stellar octangula will have the same effect.
	www-history.mcs.st-and.ac.uk /~john/geometry/Solutions/S5.html (490 words)

	Key Curriculum Press \| Visual Geometry Project (Site not responding. Last check: 2007-10-13)
		The Stella Octangula Activity Book contains flline masters for nine standalone activities that guide student inquiry into the simple-but-elegant stella octangula.
		Included are instructions for 12 independent student projects, an annotated bibliography, and flline masters for creating the models.
		The Stella Octangula Manipulative Kit contains all materials (except glue) to complete the activities in The Stella Octangula Activity Book.
	www.keypress.com /catalog/printer_friendly/supplementals/VisualGeo.html (335 words)

	Roger's Connection Magnetic Building Set! - for ages 6 to adult
		In Roger's Connection, all edge lengths (magnetic rod lengths) are the same, but in order to form a stellated icosahedron or dodecahedron, different lengths from those available would be required to add the stellations.
		Roger's Connection can be used to make only one of the stellated platonic solids, a stellated octahedron, also called a stella octangula, which has the appearance of two interlocked tetrahedrons.
		The stella octangula may be viewed and rotated at: http://mathworld.wolfram.com/StellaOctangula.html.
	www.rogersconnection.com /Movies.html (642 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		Also discusses work on the regular solids due to Johannes Kepler, including Kepler's recognition of a duality and his idea of a combination of two tetrahedra called a stella octangula.
		The author notes that the notion of the stella octangula also appears in Pacioli's De Divina Proportione.
		In addition, Kepler's stellated dodecahedron occurs in mosaics in the San Macro Cathedral in Venice; this work is thought to have been done by Paolo Uccello.
	math.truman.edu /cgi-bin/thammond/makebibnote.pl?code=aamtps (283 words)

	Stella Octangula (Site not responding. Last check: 2007-10-13)
		A Stella Octangula is a compound of two tetrahedra
		Print the picture on normal or heavy paper.
		It's permitted to make copies for non-commercial purposes only.
	www.korthalsaltes.com /stella_octangula.htm (35 words)

	Exercises 5 (Site not responding. Last check: 2007-10-13)
		Identify the dual of the stella octangula and hence find its direct and full symmetry groups.
		If we regard the stella octangula as the union of two tetrahedra T
		Describe how you would colour the stella octangula to get a figure F with S
	www-history.mcs.st-and.ac.uk /~john/geometry/Tutorials/T5.html (207 words)

	Compound Polyhedra
		The second type of compound is an interpenetrating set of several copies of the same polyhedron.
		The simplest example is the compound of two tetrahedra, called the stella octangula by Kepler.
		If we replace each of the five cubes inscribed in a dodecahedron with the two tetrahedra of its stella octangula, we get a compound of ten tetrahedra inscribed in a dodecahedron.
	www.georgehart.com /virtual-polyhedra/compounds-info.html (1372 words)

	ipedia.com: Tetrahedron Article (Site not responding. Last check: 2007-10-13)
		The volume of this tetrahedron is 1/3 the volume of the cube.
		Taking both tetrahedra within a single cube gives a regular polyhedral compound called the stella octangula, whose interior is an octahedron.
		Inscribing tetrahedra inside the regular compound of five cubes gives two more regular compounds, containing five and ten tetrahedra.
	www.ipedia.com /tetrahedron.html (336 words)

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