Curiosity: by alternating this polyhedron with a regular dodecahedron you can fill the space.
It has tetrahedral symmetry without reflection plan, thus exists in two mirror image versions.
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compound of two regular triangular prisms (prism with base a David's star) |
regular pentagrammic pyramid (base: star pentagon) |
regular pentagrammic prism (uniform polyhedron) |
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a pentagonal star (skeleton: golden triangles with same base) |
pentagrammic bipyramid (ten self intersecting equilateral triangles) |
non crossed regular pentagrammic antiprism (uniform polyhedron) |
| This uniform polyhedron, the tetrahemihexahedron, has only seven faces: four triangles and three squares going through the centre and two by two orthogonal. Its twelve edges are the sides of the four triangles. It is a one-sided non orientable surface.
This "regular" heptahedron is a regular octahedron from which four regular tri-right-angled tetrahedra have been excavated; it is also a faceted octahedron. |
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the small rhombihexahedron (uniform polyhedron) (18 faces, among which 6 self-intersecting octagons) |
and its dual: the small rhombihexacron (24 "butterfly" faces: crossed symmetric quadrilaterals) |
| The medial rhombic triacontahedron is the dual of the dodecadodecahedron which is a non convex uniform polyhedron. It is a stellation of the rhombic triacontahedron with hidden interior pentagrammic vertices. |
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The faces of this dodecahedron are identical non convex symmetrical pentagons (piece of a pentagram). It has tetrahedral symmetry with only three reflection planes two by two orthogonal.
Curiosity: by alternating this polyhedron with a regular dodecahedron you can fill the space.
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The faces of this dodecahedron described by George Olshevsky are also identical non convex pentagons cut out from an acute golden triangle: a face is the assembling of two obtuse golden triangles (one vertex of the pentagon belongs to the opposite side).
It has tetrahedral symmetry without reflection plan, thus exists in two mirror image versions.
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The net of this non convex deltahedron is also a net of the regular octahedron.
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| All the faces of these two polyhedra are equilateral triangles and all their edges belong to the symmetry planes. | |
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tetrahedral symmetry (6 symmetry planes, 24 faces) |
octahedral symmetry (9 symmetry planes, 48 faces) |
| All the faces of these two polyhedra are equilateral triangles; "pockets" ("open" bipyramids) have been assembled to build closed rings. | |
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7x(2x5) = 70 faces |
3x(2x5) + 3x(2x4) = 54 faces |
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3 triangles, 3 squares and 3 pentagons |
a toroid with 6 triangles and 6 pentagons |
| On both compounds the intersection of the three prisms is a cube; hit "f" to see this hidden cube. | |
| references: |
http://cs.stmarys.ca/~dawson/images3.html by Robert Dawson.
http://www.orchidpalms.com/polyhedra/acrohedra/543.html by Jim McNeill (author of the program Hedron ) |
| summary | January 2004 updated 08-08-2012 |