The icosahedral pyramid is a four-dimensional
convex polytope, bounded by one
icosahedron 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 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 regu ...
s meeting at an apex.
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References
External links
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* Richard Klitzing
Axial-Symmetrical Edge Facetings of Uniform PolyhedraIcosahedral pyramid
4-polytopes
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