In geometry, the gyrobifastigium is the 26th Johnson solid (J26). It can be constructed by joining two face-regular triangular prisms along corresponding square faces, giving a quarter-turn to one prism.[1] It is the only Johnson solid that can tile three-dimensional space.[2][3]
It is also the vertex figure of the nonuniform p-q duoantiprism (if p and q are greater than 2). Despite the fact that p, q = 3 would yield a geometrically identical equivalent to the Johnson solid, it lacks a circumscribed sphere that touches all vertices, except for the case p = 5,q = 5/3, which represents a uniform great duoantiprism.
Its dual, the elongated tetragonal disphenoid, can be found as cells of the duals of the p-q duoantiprisms.
^Darling, David (2004), The Universal Book of Mathematics: From Abracadabra to Zeno's Paradoxes, John Wiley & Sons, p. 169, ISBN 9780471667001.
^Cite error: The named reference ah06 was invoked but never defined (see the help page).
^Cite error: The named reference kepler was invoked but never defined (see the help page).
In geometry, the gyrobifastigium is the 26th Johnson solid (J26). It can be constructed by joining two face-regular triangular prisms along corresponding...
In geometry, the elongated gyrobifastigium or gabled rhombohedron is a space-filling octahedron with 4 rectangles and 4 right-angled pentagonal faces...
clusters. The dual polyhedron of the snub disphenoid is the elongated gyrobifastigium. The snub disphenoid can be constructed in different ways. As suggested...
and gyrobifastigium. The cube is the only Platonic solid that can tessellate space on its own, and the truncated octahedron and gyrobifastigium are the...
uniform honeycombs. Pairs of triangular prisms can be combined to create gyrobifastigium cells. The resulting honeycomb is closely related but not equivalent:...
truncated. Tetragonal trapezohedron: The eight faces are congruent kites. Gyrobifastigium: Two uniform triangular prisms glued over one of their square sides...
tessellate space as a three-dimensional analogue of the hexagon, and the gyrobifastigium, with four square faces and four triangular faces, is the only Johnson...
are stereohedra but not parallelohedra nor plesiohedra include the gyrobifastigium. Ivanov, A. B. (2001) [1994], "Stereohedron", Encyclopedia of Mathematics...
an American fighter aircraft in service with the Swedish Air Force Gyrobifastigium, a Johnson solid (J26) J26 G8 Protests, held in Calgary, Alberta in...
{5}}}}-2{\sqrt {5}}-2}}\right)a^{3}\\&\approx 13.6671a^{3}\end{aligned}}} 26 Gyrobifastigium 8 14 8 D 2 d {\displaystyle D_{2d}} of order 8 A = ( 4 + 3 ) a 2 ≈...
octahedron and self-dual octahedron. These polyhedra resemble the dual gyrobifastigium in that both shapes have eight vertices and eight faces, with the faces...
include prisms over certain quadrilaterals, pentagons, and hexagons. The gyrobifastigium is a stereohedron but not a plesiohedron, because the points at the...
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