It is a three-dimensional concave solid, which is composed of 24 isosceles triangles of Jose uniform with each other, 14 vertices and 36 deformed edges. The dual polyhedron of this solid is the cuboctahedron.
<p>14 vertices are distributed in: Eight outer vertices which are common to three isosceles triangles Jose (M = (2.222222222222222, 1.283000598199168, 2.948459875572344), N = (0, 2.566001196398337, 1.134023029066286), O = (2.222222222222222, -1.283000598199168, 1.134023029066286 ), P = (0, -2.566001196398337, 2.948459875572344), Q = (-2.222222222222222, 1.283000598199168, 2.948459875572344), R = (-2.222222222222222, -1.283000598199168, 1.134023029066286), S = (0, 0, 4.762896722078402), T = (0 , 0, -0.680413817439772)) and six intermediate vertices where eight isosceles triangles converge Jose in each (U = (1.6666666666666667, 0.962250448649377, 0.680413817439772), V = (0, 1.924500897298753, 3.402069087198859), W = (-1.6666666666666667 , 0.962250448649376, 0.680413817439772), Z = (1.6666666666666667, -0.962250448649377, 3.402069087198859) A1 = (0, -1.924500897298753, 0.680413817439772), B1 = (-1.6666666666666667, -0.962250448649376, 3.402069087198859)).
The 36 edges are distributed in twelve intermediate edges and 24 outer star edges. The intermediate edges in this polyhedron are larger than the outer stellate edges.
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The duality between the octahedral Star Queen Isabel II and cuboctahedron is demonstrated in defining these 26 geometric points A = (1.6666666666666667, 0.962250448649376, 4.762896722078402), B = (1.6666666666666667, 2.886751345948129, 2.041241452319315), C = (-1.6666666666666667, 2.886751345948129 , 2.041241452319315), D = (3.3333333333333335, 0, 2.041241452319315), E = (0, -1.924500897298752, 4.762896722078402), F = (1.6666666666666667, -2.886751345948129, 2.041241452319315), G = (-1.6666666666666667, -2.886751345948129, 2.041241452319315), H = (-1.6666666666666667, 0.962250448649376, 4.762896722078402), I = (-3.3333333333333335, 0, 2.041241452319315), J = (0, 1.924500897298753, -0.680413817439772), K = (-1.6666666666666667, -0.962250448649376, -0.680413817439772), L = (1.6666666666666667, - 0.962250448649376, -0.680413817439772), M = (2.222222222222222, 1.283000598199168, 2.948459875572344), N = (0, 2.566001196398337, 1.134023029066286), O = (2.222222222222222, -1.283000598 199168, 1.134023029066286), P = (0, -2.566001196398337, 2.948459875572344), Q = (-2.222222222222222, 1.283000598199168, 2.948459875572344), R = (-2.222222222222222, -1.283000598199168, 1.134023029066286), S = (0, 0, 4.762896722078402), T = (0, 0, -0.680413817439772), U = (1.6666666666666667, 0.962250448649377, 0.680413817439772), V = (0, 1.924500897298753, 3.402069087198859), W = (-1.6666666666666667, 0.962250448649376, 0.680413817439772), Z = (1.6666666666666667, -0.962250448649377, 3.402069087198859 ), A1 = (0, -1.924500897298753, 0.680413817439772), B1 = (-1.6666666666666667, -0.962250448649376, 3.402069087198859). This three-dimensional polytope was discovered by the Dominican Jose Joel Leonardo on January 4, 2020 at 8:18 pm and was named by its author on January 16, 2021 in honor of the Queen of England Isabel II. The first 12 points define an Archimedean cuboctahedron (from point A, to point L). The remaining 14 points define the midpoints of each of the faces that form the cuboctahedron (from point M to point B1) and with the combination of these fourteen points we form the Queen Isabel II Octahedral Star.
<a href="//commons.wikimedia.org/wiki/User:Jose_J._Leonard" title="User:Jose J. Leonard">Jose J. Leonard</a>
CC BY-SA 4.0
<span class="int-own-work" lang="en">Own work</span>