Acronym | sidtidap | ||||||||||||||||||||||||||||
Name | small-ditrigonary-icosidodecahedron antiprism | ||||||||||||||||||||||||||||
Cross sections |
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Circumradius | sqrt[(5+sqrt(5))/8] = 0.951057 | ||||||||||||||||||||||||||||
Colonel of regiment |
(is itself locally convex
– uniform polychoral members:
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Face vector | 40, 180, 184, 54 | ||||||||||||||||||||||||||||
Confer |
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External links |
As abstract polytope sidtidap is isomorphic to gidtidap, thereby replacing pentagrams by pentagons, resp. stap by pap and sidtid by gidtid.
In fact, this polychoron generalizes the idea of a 3D antiprism by way of being a snub (here: holosnub). But this figure is not what now became the accepted sense of a 4D antiprism, where its bases have to be duals of each other. It rather looks more like what was coined as cupola (in its narrower sense), i.e. the xoPoxQoo&#x segmentochora, as it uses pyramids and antiprisms for lacing facets only. (But pyramids do point here in both directions, so.)
Incidence matrix according to Dynkin symbol
β2β5o3o both( . . . . ) | 40 | 3 6 | 3 9 3 | 3 1 4 ----------------+----+--------+-----------+-------- both( s2s . . ) | 2 | 60 * | 0 4 0 | 2 0 2 sefa( . β5o . ) | 2 | * 120 | 1 1 1 | 1 1 1 ----------------+----+--------+-----------+-------- . β5o . ♦ 5 | 0 5 | 24 * * | 1 1 0 sefa( β2β5o . ) | 3 | 2 1 | * 120 * | 1 0 1 sefa( . β5o3o ) | 3 | 0 3 | * * 40 | 0 1 1 ----------------+----+--------+-----------+-------- β2β5o . ♦ 10 | 10 10 | 2 10 0 | 12 * * . β5o3o ♦ 20 | 0 60 | 12 0 20 | * 2 * sefa( β2β5o3o ) ♦ 4 | 3 3 | 0 3 1 | * * 40 starting figure: x x5o3o
xo5/2ox3oo3*a&#x → height = sqrt[(sqrt(5)-1)/2] = 0.786151
(sidtid || gyro sidtid)
o. o. o. | 20 * | 6 3 0 | 3 3 6 3 0 0 | 1 3 3 1 0
.o .o .o | * 20 | 0 3 6 | 0 0 3 6 3 3 | 0 3 1 3 1
-----------------+-------+----------+-------------------+-------------
x. .. .. | 2 0 | 60 * * | 1 1 1 0 0 0 | 1 1 1 0 0
oo5/2oo3oo3*a&#x | 1 1 | * 60 * | 0 0 2 2 0 0 | 0 2 1 1 0
.. .x .. | 0 2 | * * 60 | 0 0 0 1 1 1 | 0 1 0 1 1
-----------------+-------+----------+-------------------+-------------
x.5/2o. .. | 5 0 | 5 0 0 | 12 * * * * * | 1 1 0 0 0
x. .. o.3*a | 3 0 | 3 0 0 | * 20 * * * * | 1 0 1 0 0
xo .. .. &#x | 2 1 | 1 2 0 | * * 60 * * * | 0 1 1 0 0
.. ox .. &#x | 1 2 | 0 2 1 | * * * 60 * * | 0 1 0 1 0
.o5/2.x .. | 0 5 | 0 0 5 | * * * * 12 * | 0 1 0 0 1
.. .x3.o | 0 3 | 0 0 3 | * * * * * 20 | 0 0 0 1 1
-----------------+-------+----------+-------------------+-------------
x.5/2o.3o.3*a ♦ 20 0 | 60 0 0 | 12 20 0 0 0 0 | 1 * * * *
xo5/2ox .. &#x ♦ 5 5 | 5 10 5 | 1 0 5 5 1 0 | * 12 * * *
xo .. oo3*a&#x ♦ 3 1 | 3 3 0 | 0 1 3 0 0 0 | * * 20 * *
.. ox3oo &#x ♦ 1 3 | 0 3 3 | 0 0 0 3 0 1 | * * * 20 *
.o5/2.x3.o3*a ♦ 0 20 | 0 0 60 | 0 0 0 0 12 20 | * * * * 1
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