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Rectangular cuboid shapes are often used for boxes, cupboards, rooms, buildings, containers, cabinets, books, sturdy computer chassis, printing devices, electronic calling touchscreen devices, washing and drying machines, etc. They are among those solids that can
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Webb, Charlotte; Smith, Cathy (2013). "Developing subject knowledge". In Lee, Clare; Johnston-Wilder, Sue; Ward-Penny, Robert (eds.).
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is an Euler brick whose space diagonal is also an integer. It is currently unknown whether a perfect cuboid actually exists.
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596:. However, this number increases significantly to at least 54 for a rectangular cuboid of three different lengths.
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565:. The shape is fairly versatile in being able to contain multiple smaller rectangular cuboids, e.g.
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faces. These are often called "cuboids", without qualifying them as being rectangular, but a
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A rectangular cuboid with integer edges, as well as integer face diagonals, is called an
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620:— a problem asking the shortest path between two points on a cuboid's surface.
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213:, the resulting one may obtain another special case of rectangular prism, known as
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in a box, boxes in a cupboard, cupboards in a room, and rooms in a building.
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205:. Rectangular cuboids may be referred to colloquially as "boxes" (after the
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rectangular face, then calculating the hypotenuse's length using the
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A square rectangular prism, a special case of the rectangular prism.
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1059:
318:
its volume is the product of the rectangular area and its height:
28:
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1426:
1020:
A Practical Guide to
Teaching Mathematics in the Secondary School
806:
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650:, however, are ambiguous, since they do not specify all angles.
210:
179:
145:
109:
247:. In the case that all six faces are squares, the result is a
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can also refer to a more general class of polyhedra, with six
157:
614:— a measurement of a cuboid in which all points exist;
1119:
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420:
can be found by constructing a right triangle of height
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its surface area is the sum of the area of all faces:
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A cube, a special case of the square rectangular box.
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Cuboid with all right angles and equal opposite faces
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671:. However, this is sometimes ambiguously called a
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1034:
545:{\displaystyle d={\sqrt {a^{2}+b^{2}+c^{2}}}.}
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965:Pisanski, Tomaž; Servatius, Brigitte (2013).
581:; for example with sides 44, 117, and 240. A
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27:
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968:Configuration from a Graphical Viewpoint
917:Science and Mathematics for Engineering
888:
1476:
934:
854:
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608:— generalization of a rectangle;
1063:
1035:
994:Robertson, Stewart Alexander (1984).
440:with its base as the diagonal of the
1089:
944:Mills, Steve; Kolf, Hillary (1999).
937:Elements of Synthetic Solid Geometry
913:
845:
785:
572:
254:If a rectangular cuboid has length
13:
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563:tessellate three-dimensional space
228:
14:
1500:
1028:
907:
217:. They can be represented as the
198:. By definition, this makes it a
935:Dupuis, Nathan Fellowes (1893).
209:). If two opposite faces become
190:of a rectangular cuboid are all
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144:
882:
811:Pisanski & Servatius (2013)
1002:. Cambridge University Press.
836:
767:
678:
653:
636:
618:The spider and the fly problem
407:{\displaystyle A=2(ab+ac+bc).}
398:
371:
1:
889:Steward, Don (May 24, 2013).
624:
555:
194:, and its opposite faces are
135:
1462:Degenerate polyhedra are in
1054:Rectangular prism and cuboid
745:
124:. This shape is also called
7:
1281:pentagonal icositetrahedron
1222:truncated icosidodecahedron
920:(6th ed.). Routledge.
599:
10:
1505:
1311:pentagonal hexecontahedron
1271:deltoidal icositetrahedron
170:A rectangular cuboid is a
126:rectangular parallelepiped
116:faces in which all of its
1460:
1394:
1369:
1351:
1344:
1319:
1306:disdyakis triacontahedron
1301:deltoidal hexecontahedron
1235:
1143:
1098:
1056:Paper models and pictures
977:10.1007/978-0-8176-8364-1
215:square rectangular cuboid
130:orthogonal parallelepiped
82:
72:
62:
49:
35:
26:
21:
704:{\displaystyle \Pi _{n}}
629:
588:The number of different
240:{\displaystyle \Pi _{4}}
1412:gyroelongated bipyramid
1286:rhombic triacontahedron
1192:truncated cuboctahedron
873:Webb & Smith (2013)
827:Mills & Kolf (1999)
108:is a special case of a
1407:truncated trapezohedra
1276:disdyakis dodecahedron
1242:(duals of Archimedean)
1217:rhombicosidodecahedron
1207:truncated dodecahedron
998:Polytopes and Symmetry
730:
705:
546:
475:
455:
434:
408:
347:
346:{\displaystyle V=abc.}
308:
288:
268:
241:
1296:pentakis dodecahedron
1212:truncated icosahedron
1167:truncated tetrahedron
731:
706:
547:
476:
456:
435:
409:
348:
309:
289:
269:
242:
1256:rhombic dodecahedron
1182:truncated octahedron
720:
688:
659:This is also called
612:Minimum bounding box
490:
465:
445:
424:
359:
322:
298:
278:
258:
224:
1291:triakis icosahedron
1266:tetrakis hexahedron
1251:triakis tetrahedron
1187:rhombicuboctahedron
914:Bird, John (2020).
484:Pythagorean theorem
1261:triakis octahedron
1146:Archimedean solids
1037:Weisstein, Eric W.
891:"nets of a cuboid"
726:
701:
669:right square prism
542:
471:
451:
430:
404:
343:
304:
284:
264:
237:
200:right rectangular
106:rectangular cuboid
22:Rectangular cuboid
1471:
1470:
1390:
1389:
1227:snub dodecahedron
1202:icosidodecahedron
986:978-0-8176-8363-4
957:978-0-435-02474-1
927:978-0-429-26170-1
729:{\displaystyle n}
644:rectangular prism
594:simple cube is 11
573:Related polyhedra
537:
474:{\displaystyle b}
454:{\displaystyle a}
433:{\displaystyle c}
307:{\displaystyle c}
287:{\displaystyle b}
267:{\displaystyle a}
172:convex polyhedron
102:
101:
1496:
1349:
1348:
1345:Dihedral uniform
1320:Dihedral regular
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947:Maths Dictionary
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758:Robertson (1984)
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1395:Dihedral others
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1340:
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1139:
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1100:Platonic solids
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711:represents the
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207:physical object
188:dihedral angles
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118:dihedral angles
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12:
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5:
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1298:
1293:
1288:
1283:
1278:
1273:
1268:
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1253:
1247:
1245:
1238:Catalan solids
1236:
1233:
1232:
1230:
1229:
1224:
1219:
1214:
1209:
1204:
1199:
1194:
1189:
1184:
1179:
1177:truncated cube
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1132:
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1029:External links
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908:Bibliographies
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606:Hyperrectangle
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583:perfect cuboid
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1489:Orthogonality
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1172:cuboctahedron
1170:
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1009:9780521277396
1005:
1000:
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992:
988:
982:
978:
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969:
963:
959:
953:
950:. Heinemann.
949:
948:
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938:
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929:
923:
919:
918:
912:
911:
892:
885:
878:
874:
869:
860:
856:
855:Dupuis (1893)
853:
851:
847:
844:
843:
839:
832:
828:
823:
816:
812:
807:
805:
795:
791:
787:
784:
782:
778:
777:Dupuis (1893)
775:
774:
770:
763:
759:
754:
750:
723:
714:
696:
681:
674:
670:
666:
662:
661:square cuboid
656:
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635:
619:
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603:
597:
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448:
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340:
337:
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331:
328:
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317:
316:
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301:
294:, and height
281:
261:
252:
250:
232:
220:
216:
212:
208:
204:
203:
197:
193:
189:
185:
184:quadrilateral
181:
177:
173:
159:
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111:
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41:
38:
34:
30:
25:
20:
1463:
1382:trapezohedra
1333:
1326:
1130:dodecahedron
1043:
1023:. Routledge.
1019:
997:
971:. Springer.
967:
946:
939:. Macmillan.
936:
916:
894:. Retrieved
884:
868:
838:
822:
769:
753:
738:sided prism.
680:
673:square prism
672:
668:
664:
660:
655:
648:oblong prism
647:
643:
638:
587:
576:
559:
253:
214:
199:
192:right angles
169:
129:
125:
122:right angles
105:
103:
44:Plesiohedron
1152:semiregular
1135:icosahedron
1115:tetrahedron
896:December 1,
846:Bird (2020)
786:Bird (2020)
684:The symbol
579:Euler brick
567:sugar cubes
219:prism graph
186:faces. The
114:rectangular
1478:Categories
1447:prismatoid
1377:bipyramids
1361:antiprisms
1335:hosohedron
1125:octahedron
875:, p.
857:, p.
848:, p.
829:, p.
813:, p.
788:, p.
779:, p.
760:, p.
665:square box
642:The terms
625:References
556:Appearance
136:Properties
92:zonohedron
83:Properties
57:rectangles
1442:birotunda
1432:bifrustum
1197:snub cube
1092:polyhedra
1045:MathWorld
746:Citations
693:Π
229:Π
196:congruent
176:rectangle
174:with six
1422:bicupola
1402:pyramids
1328:dihedron
1040:"Cuboid"
713:skeleton
600:See also
314:, then:
274:, width
97:isogonal
74:Vertices
1484:Cuboids
1464:italics
1452:scutoid
1437:rotunda
1427:frustum
1156:uniform
1105:regular
1090:Convex
792:–
211:squares
1417:cupola
1370:duals:
1356:prisms
1006:
983:
954:
924:
592:for a
180:cuboid
110:cuboid
87:convex
715:of a
667:, or
630:Notes
202:prism
112:with
64:Edges
51:Faces
40:Prism
1120:cube
1004:ISBN
981:ISBN
952:ISBN
922:ISBN
898:2018
646:and
590:nets
461:-by-
416:its
249:cube
120:are
36:Type
1154:or
973:doi
877:108
850:144
794:144
790:143
128:or
1480::
1042:.
979:.
859:82
831:16
815:21
803:^
781:68
762:75
663:,
486::
251:.
132:.
104:A
68:12
55:6
1466:.
1158:)
1150:(
1107:)
1103:(
1083:e
1076:t
1069:v
1048:.
1012:.
989:.
975::
960:.
930:.
900:.
879:.
833:.
817:.
764:.
736:-
724:n
697:n
675:.
540:.
533:2
529:c
525:+
520:2
516:b
512:+
507:2
503:a
497:=
494:d
469:b
449:a
428:c
402:.
399:)
396:c
393:b
390:+
387:c
384:a
381:+
378:b
375:a
372:(
369:2
366:=
363:A
341:.
338:c
335:b
332:a
329:=
326:V
302:c
282:b
262:a
233:4
94:,
89:,
78:8
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