The icosahedral pyramid is a four-dimensional
convex polytope, bounded by one
icosahedron
In geometry, an icosahedron ( or ) is a polyhedron with 20 faces. The name comes and . The plural can be either "icosahedra" () or "icosahedrons".
There are infinitely many non- similar shapes of icosahedra, some of them being more symmetric ...
as its base and by 20
triangular pyramid
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ...
cells
Cell most often refers to:
* Cell (biology), the functional basic unit of life
Cell may also refer to:
Locations
* Monastic cell, a small room, hut, or cave in which a religious recluse lives, alternatively the small precursor of a monastery w ...
which meet at its apex. Since an icosahedron's circumradius is less than its edge length,
[, circumradius sqrt 5+sqrt(5))/8 = 0.951057] the tetrahedral pyramids can be made with regular faces.
Having all regular cells, it is a Blind polytope. Two copies can be augmented to make an icosahedral bipyramid which is also a Blind Polytope.
The regular 600-cell has icosahedral pyramids around every vertex.
The dual to the icosahedral pyramid is the dodecahedral pyramid, seen as a dodecahedron, dodecahedral base, and 12 regular
pentagonal pyramid
In geometry, a pentagonal pyramid is a pyramid with a pentagonal base upon which are erected five triangular faces that meet at a point (the apex). Like any pyramid, it is self- dual.
The ''regular'' pentagonal pyramid has a base that is a reg ...
s meeting at an apex.
:
References
External links
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*
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* Richard Klitzing
Axial-Symmetrical Edge Facetings of Uniform PolyhedraIcosahedral pyramid
4-polytopes
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