- Gyrobifastigium
Infobox_Polyhedron
Polyhedron_Type=Johnson
"J"25 - J26 - J27
Face_List=4triangle s
4 squares
Edge_Count=14
Vertex_Count=8
Symmetry_Group="D"2d
Vertex_List=4(3.42)
4(3.4.3.4)
Dual=-
Property_List=convexIn
geometry , the gyrobifastigium is the 26thJohnson solid ("J"26). It can be constructed by joining two face-regular triangular prisms along corresponding square faces, giving a half-turn to one prism.The name comes from the Latin "fastigium", meaning a sloping roof. [ [http://penelope.uchicago.edu/Thayer/E/Roman/Texts/secondary/SMIGRA*/Fastigium.html William Smith, D.C.L., LL.D.: A Dictionary of Greek and Roman Antiquities, John Murray, London, 1875] ] In the standard naming convention of the Johnson solids, "bi-" means two solids connected at their bases, and "gyro-" means the two halves are twisted with respect to each other.
The gyrobifastigium's place in the list of Johnson solids, immediately before the bicupolas, is explained by viewing it as a "digonal gyrobicupola". Just as the other regular cupolas have an alternating sequence of squares and triangles surrounding a single polygon at the top (triangle, square or pentagon), each half of the gyrobifastigium consists of just alternating squares and triangles, connected at the top only by a ridge.
The 92 Johnson solids were named and described by
Norman Johnson in1966 .References
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