# Digonal gyrobicupolic ring (EntityTopic, 17)

The digonal gyrobicupolic ring, or K4.8, is a member of the set of bicupolic rings. Its cells are 1 tetrahedron, 4 square pyramids and 2 triangular prisms. Its faces are 1+4 squares and 4+4+4 triangles. It has 2+4+4+8 edges and 4+4 vertices.

Keiji studied it explicitly to try to understand more about the segmentochora.

## Construction

It is possible to construct the digonal gyrobicupolic ring from three different pairs of polytopes: Petrie polygon Square pyramid andopposite triangle highlighted Tetrahedron andopposite square highlighted Triangular prism andopposite digon highlighted

This segmentochoron also arises from a bidiminishing of the pyrorectichoron. First, delete any vertex from the pyrorectichoron. That forms the (mono)diminished pyrorectichoron, better known as the trigonal biantiprismatic ring, or K4.6; its cells are 1 triangular prism, 2 octahedra, 3 square pyramids, and 3 tetrahedra. It can be constructed as trigonal prism || gyrated triangle; if a vertex from the gyrated triangle is deleted, it will create a second triangular prism, thus resulting in this segmentochoron.

## Projections

The following projection shows this segmentochoron from a viewpoint analogous to that of the other bicupolic rings, to show how the gyrated digons connect to each other via a tetrahedron (digon antiprism) and to the opposite square face via triangular prisms (digon cupolae). ## Incidence matrix

Dual: K4.8 dual

 # TXID Type Name Va Vb Ea Eb Ec Ed 3a 3b 3c 4a 4b C1a C2a C3a 0 Va = point ; 1 Vb = point ; 2 Ea 2 0 = digon ; 3 Eb 1 1 = digon ; 4 Ec 0 2 = digon ; 5 Ed 0 2 = digon ; 6 3a 2 1 1 2 0 0 = triangle ; 7 3b 1 2 0 2 1 0 = triangle ; 8 3c 0 3 0 0 2 1 = triangle ; 9 4a 4 0 0 0 4 0 = square ; 10 4b 2 2 1 2 0 1 = square ; 11 C1a 4 2 4 4 0 1 2 0 0 1 2 = triangular prism ; 12 C2a 2 3 1 4 2 1 1 2 1 0 1 = square pyramid ; 13 C3a 0 4 0 0 4 2 0 0 4 0 0 = tetrahedron ; 14 H4.1a 4 4 4 8 4 2 4 4 4 1 4 2 4 1 = K4.8 ;

## Usage as facets

This polytope does not currently appear as facets in any higher-dimensional polytopes in the database.