Gyrobifastigium

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 half-turn to one prism.

The name comes from the Latin fastigium, meaning a sloping roof. 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 in 1966.

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