:Rhombic hectotriadiohedron

{{more citations needed|date=April 2025}}

{{infobox polyhedron

| name = Rhombic hectotriadiohedron

| image = 130px130px

| caption = Two different types: Type T and Type C, respectively

| type = zonohedron

| faces = 132 rhombi

| edges = 264

| vertices = 134

| symmetry = octahedral symmetry $\backslash mathrm\{O\}\_\backslash mathrm\{h\}$

| properties = convex

}}

In geometry, a rhombic hectotriadiohedron, rhombhectotriadiohedron,{{r|wb}} rhombic 132-hedron, or equilateral dodecazonohedron{{r|hanegraaf}} is a polyhedron composed of 132 rhombic faces. Rhombic faces have five positions within octahedral symmetry.{{citation

| title = Twenty Questions on Zonogons, Zonohedra and Zonoids

| year = 1980

| last = Hanegraaf | first = Anton

| url = https://www.iri.upc.edu/people/ros/StructuralTopology/ST4/st4-08-a4-ocr.pdf

| publisher = Université du Quebéc à Montréal

| pages = 31–40

}}. There are two topological types, with the same number of elements and the same symmetry but with a somewhat different arrangement of rhombic faces.{{citation

| url = http://www.scipress.org/e-library/rpf/pdf/chap2/0055.PDF

| title = Derivation of Some Equilateral Zonohedra and Star Zonohedra

| last1 = Watanabe | first1 = Y.

| last2 = Betsumiya | first2 = T.

| publisher = Research of pattern formation

| archive-url = https://web.archive.org/web/20161125110103/http://www.scipress.org/e-library/rpf/pdf/chap2/0055.PDF

| archive-date = 2016-11-25

}}.

There are two types of rhombic hectotridiohedron: the type T and C. The type T has eight rhombi meeting at the center of a cube's six faces. The three meet at the 8 corners of a cube. The twelve are positioned along the twelve edges of a cube, and four more surround each of the twelve edges of a cube. This polyhedron is a 12-zone zonohedrification{{Cite web|url=http://www.georgehart.com/virtual-polyhedra/zonohedrification.html|title=Zonohedrification}} of the rhombicuboctahedron.{{Cite web|url=http://www.georgehart.com/virtual-polyhedra/zonohedra-index.html|title = Zonohedra --- List}}{{better citation needed|date=March 2025}} The type C is a 12-zone zonohedrification of a truncated cube.{{cn|date=March 2025}}