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Koch 1972 Koch, Elke, Wirkungsbereichspolyeder und
Wirkungsbereichsteilunger zukubischen Gitterkomplexen mit weniger als drei Freiheitsgraden (Efficiency Polyhedra, and Efficiency Dividers, cubic lattice complexes with less than three degrees of freedom) Dissertation, University Marburg/Lahn 1972 -
241:, except two edges from the original tetrahedron are reduced to zero length making pentagonal faces. The dual polyhedra can be called a skew-truncated tetragonal disphenoid, where 2 edges along the symmetry axis completely truncated down to the edge midpoint.
208:
If the space-filling polyhedron is placed in a 3-D coordinate grid, the coordinates for the 8 vertices can be given as: (0, ±2, −1), (±2, 0, 1), (±1, 0, −1), (0, ±1, 1).
51:
699:, with alternate cells removed and augmented into neighboring cells by a center vertex. The rhombic faces in the honeycomb are aligned along 3 orthogonal planes.
1258:
symmetry. These paired-cells stack more easily as inter-locking elements. Long sequences of these can be stacked together in 3 axes to fill space.
533:
471:
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for its cross-sectional appearance. The two right-most symmetric projections below show the rhombi edge-on on the top, bottom and a middle
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200:(diamond-shaped) faces. He catalogued it in a 1982 paper as 10-II, the second in a list of 26 known space-filling decahedra.
1008:
with 6 vertices, 10 edges, and 6 faces (4 triangles, 2 right trapezoids). Michael
Goldberg identifies this polyhedron as an
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997:
with 6 vertices, 11 edges, and 7 faces (6 triangles and 1 trapezoid). Michael
Goldberg identifies this polyhedron as a
907:
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181:
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970:
cross-section between the two rhombic faces. It is a decahedron with 12 vertices, 20 edges, and 10 faces (4
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317:
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symmetry, which projects as order-4 dihedral (square) symmetry in two dimensions. It can be seen as a
453:
274:
265:
911:
288:
234:
192:
because its faces are not composed entirely of regular polygons. Michael
Goldberg named it after a
91:
986:). Michael Goldberg labels this polyhedron 10-XXV, the 25th in a list of space-filling decahedra.
444:
185:
1327:
1320:
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1085:
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352:
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It can be further dissected as a quarter-model by another symmetry plane into a space-filling
902:
127:
1226:
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1078:
448:
303:
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237:, with two pairs of coplanar triangles merged into rhombic faces. The dual is similar to a
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1111:
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153:
117:
99:
17:
1427:
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184:
with 10 faces, 2 opposite rhombi with orthogonal major axes, connected by 8 identical
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189:
283:
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where the two halves are connected. The 2D projections can look convex or concave.
429:
193:
994:
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440:
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1254:
It has 12 vertices, 28 edges, and 18 faces (16 triangles and 2 rhombi) within D
1005:
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312:
993:
can be dissected as a half-model on a symmetry plane into a space-filling
1162:
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173:
105:
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979:
967:
197:
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110:
343:
1001:, type 7-XXIV, the 24th in a list of space-fillering heptahedra.
1392:
Geometriae
Dedicata, June 1978, Volume 7, Issue 2, pp 175–184
26:
1012:, type 6-X, the 10th in a list of space-filling hexahedron.
951:
Honeycomb structure orthogonally viewed along cubic plane
1411:
Geom. Dedicata, June 1977, Volume 6, Issue 1, pp 99–108
47:
1269:
on the rhombi can be done with 2 unit translation in
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243:
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84:
42:
may be too technical for most readers to understand
1428:Bowties: A Novel Class of Space Filling Polyhedron
1365:. Structural Topology, 1982, num. Type 10-II
196:, as a 10-faced polyhedron with two opposite
8:
933:Dual honeycomb of icosahedra and tetrahedra
346:
1225:
1147:
1016:Dissected models in symmetric projections
188:faces. Although it is convex, it is not a
90:
1280:(±1/2, 0, −1), (0, ±1/2, 0), (±1/2, 0, 1)
262:
70:Learn how and when to remove this message
54:, without removing the technical details.
1354:
1138:
657:Cells can be seen as the cells of the
576:alternated bitruncated cubic honeycomb
534:alternated bitruncated cubic honeycomb
472:Alternated bitruncated cubic honeycomb
81:
52:make it understandable to non-experts
7:
1285:Bow-tie model (two ten-of-diamonds)
1277:(0, ±1, −1), (±1, 0, 0), (0, ±1, 1),
999:triply truncated quadrilateral prism
618:of this honeycomb are their duals –
158:Skew-truncated tetragonal disphenoid
25:
1261:The 12 vertex coordinates in a 2-
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1390:On the space-filling heptahedra
1239:can be attached as a nonconvex
1010:ungulated quadrilateral pyramid
958:Related space-filling polyhedra
924:tetragonal disphenoid honeycomb
659:tetragonal disphenoid honeycomb
477:
467:
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1409:On the space-filling hexahedra
1363:On the Space-filling Decahedra
491:is used in the honeycomb with
1:
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1426:Robert Reid, Anthony Steed
908:Bitruncated cubic honeycomb
1469:
1377:On Space-filling Decahedra
942:Ten-of-diamonds honeycomb
899:
347:Ten-of-diamonds honeycomb
178:ten-of-diamonds decahedron
85:Ten-of-diamonds decahedron
18:Ten of diamonds decahedron
1343:Elongated gyrobifastigium
1292:
1224:
1146:
853:
713:
329:
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255:
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182:space-filling polyhedron
1453:Space-filling polyhedra
1243:space-filler, called a
966:can be dissected in an
612:tetragonal disphenoidal
580:pyritohedral icosahedra
532:, being the dual of an
652:tetragonal disphenoids
1439:Model 10/8–1, 28–404.
318:Truncated tetrahedron
245:Symmetric projection
239:truncated tetrahedron
912:truncated octahedral
1361:Goldberg, Michael.
1286:
1017:
289:triakis tetrahedron
246:
235:triakis tetrahedron
1407:Goldberg, Michael
1388:Goldberg, Michael
1284:
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244:
186:isosceles triangle
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1333:
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1122:v=12, e=20, f=10
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16:(Redirected from
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984:isotoxal octagon
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714:Dual alternated
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481:Cell-transitive
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333:v=12, e=18, f=8
330:v=10, e=16, f=8
327:v=8, e=18, f=12
324:v=8, e=16, f=10
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250:Ten of diamonds
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1237:ten-of-diamonds
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1128:v=6, e=10, f=6
1125:v=6, e=11, f=7
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991:ten-of-diamonds
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578:fills space by
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493:Coxeter diagram
489:ten-of-diamonds
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415:Ten-of-diamonds
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367:Coxeter diagram
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353:Schläfli symbol
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227:ten-of-diamonds
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154:Dual polyhedron
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48:help improve it
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1379:, type 10-XXV.
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1245:rhombic bowtie
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1195:Symmetry group
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616:vertex figures
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1267:augmentations
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1213:space-filling
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40:This article
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614:tetrahedra,
575:
574:. Since the
488:
486:
430:dodecahedron
299:Solid faces
270:Solid faces
226:
224:
207:
194:playing card
177:
171:
66:
57:
41:
1398:type 7-XXIV
1265:. (further
1031:half model
1029:Heptahedral
1026:half model
995:heptahedron
711:Alternated
620:pyritohedra
434:tetrahedron
204:Coordinates
1349:References
1293:Symmetric
1210:Properties
1062:, order 2
1055:, order 2
1048:, order 4
1034:Hexahedral
1024:Decahedral
1006:hexahedron
976:trapezoids
478:Properties
163:Properties
60:April 2017
1263:unit cube
1235:Pairs of
1205:, order 8
1163:triangles
1119:Elements
1041:Symmetry
1021:Relation
972:triangles
968:octagonal
445:Fibrifold
340:Honeycomb
148:, order 8
106:triangles
1447:Category
1417:type 6-X
1337:See also
1185:Vertices
982:, and 1
896:{4,3,4}
851:{4,3,4}
806:{4,3,4}
761:{4,3,4}
705:Uniform
361:{4,3,4}
259:Related
253:Related
221:Symmetry
174:geometry
128:Vertices
1241:bow-tie
980:rhombus
449:Coxeter
198:rhombic
46:Please
1168:rhombi
1067:Edges
914:cells
610:, and
308:Edges
279:Edges
176:, the
111:rhombi
1175:Edges
1157:Faces
708:Dual
458:(204)
441:Space
256:Dual
229:has D
180:is a
118:Edges
100:Faces
1430:2003
1290:Skew
1249:neck
1093:Net
989:The
978:, 1
974:, 4
962:The
650:and
487:The
468:Dual
412:Cell
225:The
1415:PDF
1396:PDF
1273:.)
1219:Net
1161:16
910:of
894:1,2
892:dht
849:1,2
804:1,2
759:1,2
359:1,2
357:dht
172:In
50:to
1449::
1256:2h
1202:2h
1189:12
1179:28
1166:2
1046:2v
847:ht
802:dt
661:,
654:.
622:,
582:,
536:,
463:]
231:2d
145:2d
122:16
109:2
104:8
1271:z
1200:D
1060:2
1058:C
1053:s
1051:C
1044:C
757:t
461:8
456:3
454:I
143:D
132:8
73:)
67:(
62:)
58:(
44:.
20:)
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