Dodecahedral bipyramid

{{short description|4-D convex polytope}}

{{unref |date=April 2024}}

{{Infobox 4-polytope

| Name =

| Image_File = Dodecahedral_bipyramid-ortho.png

| Image_Caption = Ortogonal projection
{{legend|red|Central dodecahedron vertices (20)}} {{legend|yellow|Apex vertices (2)}}

| Type = Polyhedral bipyramid

| Schläfli = {{nowrap|{5,3} + { } }}
dt{2,3,5}

| CD = {{CDD|node_f1|2x|node_f1|5|node|3|node}}

| Cell_List = 24 {5}∨{ } 30px

| Face_List = 60 Isosceles triangles
12 pentagons

| Edge_Count = 70 {{nowrap|(30 + 20 + 20)}}

| Vertex_Count = 22

| Vertex_Figure =

| Petrie_Polygon =

| Coxeter_Group =

| Symmetry_Group = [2,5,3], order 240

| Dual = Icosahedral prism

| Property_List = convex, isochoric

| Index =

}}

In 4-dimensional geometry, the dodecahedral bipyramid is the direct sum of a dodecahedron and a segment, {{nowrap|{5,3} + { }.}} Each face of a central dodecahedron is attached with two pentagonal pyramids, creating 24 pentagonal pyramidal cells, 72 isosceles triangular faces, 70 edges, and 22 vertices. A dodecahedral bipyramid can be seen as two dodecahedral pyramids augmented together at their base.

It is the dual of a icosahedral prism.